Before OWEN, Chief Judge, SMITH and GRAVES, Circuit Judges. JERRY E. SMITH, Circuit Judge: The district court granted Twin City Fire Insurance Company (“Twin City”) summary judgment on the claim of HM International, L.L.C. (“HMI”), that Twin City had breached its duty to indemnify. The court interpreted the policy as not covering settlement payments made after limitations for the underlying negligent conduct had expired. But properly interpreted, the policy does cover such settlement payments. We vacate and remand. I. This insurance dispute arises out of the settlement of a threatened negligence suit against HMI, which provides various accounting and financial services for Greg and Kathy Geib. On January 12, 2015, HMI’s CFO received an email from a fraudster purporting to be Greg Geib, instructing HMI to wire transfer $1 million to another bank account. HMI, unfortunately, executed the order, causing the Geibs to lose the $1 million, much of which they have been unable to recover. The fraud was discovered two days later when the fraudster attempted the scheme a second time, prompting HMI to contact Greg Geib to confirm the transfer request. Three months later, the Geibs’ attorney sent HMI a letter accusing it of negligence and demanding that HMI compensate the Geibs for their loss. HMI notified Twin City, its insurer, of the letter and requested that Twin City provide a defense and indemnification per the Directors, Officers, and Entity Liability Coverage (“D&O Policy”) held by HMI’s parent company.[1] The details of that policy are discussed infra, but, in short, the policy requires the insurer to defend and indemnify certain threatened and actual lawsuits against the insured. Twin City declined to defend HMI, citing two exclusions to the D&O policy. Shortly thereafter, HMI sued Twin City for breach of the insurance contract. The Geibs joined the lawsuit as plaintiffs against Twin City, asserting that a different part of the insurance policy separately covered them.[2] While the litigation against Twin City was ongoing, HMI and the Geibs settled their dispute. HMI paid the Geibs $470,000 and received a complete release from any liability and the right to pursue recovery of the stolen funds. The Geibs never filed their threatened negligence suit against HMI. And the settlement occurred more than two years after the Geibs’ negligence claim accrued, so limitations had run. After discovery, both HMI and Twin City moved for summary judgment. Among other contentions, Twin City theorized that it does not have to indemnify HMI for its settlement payment to the Geibs because the policy does not cover settlements made after the limitations period had run. The district court agreed with Twin City’s interpretation of the policy and granted it summary judgment on HMI’s claim for breach of the duty to indemnify. Later, on a motion to reconsider, the district court granted HMI summary judgment on its claim for breach of the duty to defend, a decision that Twin City did not cross-appeal. HMI then voluntarily dismissed its remaining claims with prejudice and appealed the district court’s grant of summary judgment to Twin City. Our review is de novo. Davis v. Fernandez, 798 F.3d 290, 292 (5th Cir. 2015). II. Under Texas law, insurance policies are interpreted “under the well-established rules of contract construction.” Great Am. Ins. Co. v. Primo, 512 S.W.3d 890, 892 (Tex. 2017). “[E]very contract should be interpreted as a whole and in accordance with the plain meaning of its terms.” Id. Courts are to “assign terms their ordinary and generally accepted meaning unless the contract directs otherwise.” Id. at 893. The policy should be interpreted so that “no provision is rendered meaningless,” and courts must “refuse to insert language or provisions the parties did not use.” Id. If the policy is ambiguous, then it is to be “interpreted in favor of coverage.” Gilbert Tex. Constr., L.P. v. Underwriters at Lloyd’s London, 327 S.W.3d 118, 133 (Tex. 2010). The D&O Policy says that “the Insurer shall pay Loss on behalf of an Insured Entity resulting from an Entity Claim first made against such Insured Entity during the Policy Period or Extended Reporting Period, if applicable, for a Wrongful Act by an Insured Entity.” (Emphasis added.) The policy defines a number of those terms, as well as some terms used in those definitions: “Loss” is defined as “Defense Costs and Damages.” “Damages” is defined as “the amounts, other than Defense Costs, that the Insureds are legally liable to pay solely as a result of a Claim covered by this Liability Coverage Part, including: . . . settlement amounts.” (Emphasis added.) “Claim” is defined to include any “Entity Claim.” “Entity Claim” is defined to be any of the following things asserted against an Insured Entity: A “written demand for monetary damages or other civil non-monetary relief commenced by the receipt of such demand”; A “civil proceeding, including arbitration or other alternative dispute proceeding, commenced by the service of a complaint, filing of a demand for arbitration, or similar pleading”; A “criminal proceeding commenced by the return of an indictment, or formal administrative or regulatory proceeding commenced by the filing of a notice of charges, or similar document.” The district court granted summary judgment to Twin City, concluding that the settlement payment was not a “loss” because it was not an amount that HMI was “legally liable to pay solely as a result of a claim.” Specifically, the court reasoned “[i]n the very sense of the words ‘legally liable,’ a claim barred by the statute of limitations cannot be a claim in which HMI faced legal liability—the law actually bars liability.” That conscientious reasoning is erroneous for two key reasons.[3] First, the district court did not account for the policy’s definition of the term “claim,” instead treating it as synonymous with “cause of action.” That error is apparent from the court’s referring to a “claim barred by the statute of limitations.” A cause of action can certainly be time-barred by a statute of limitations. But the policy’s definition of “claim” includes a “written demand for monetary damages or other civil non-monetary relief”—i.e., a Demand Letter—which cannot. Second, the district court interpreted the phrase “legally liable to pay” to mean effectively that HMI actually lost or would have lost had the Geibs filed suit. The court’s reasoning that HMI was not “legally liable to pay” the claim because HMI likely would have won based on limitations if the Geibs sued demonstrates its use of that interpretation. But under Texas law, “legally liable to pay” can mean a contractual obligation to pay. Comsys Info. Tech. Servs. v. Twin City Fire Ins. Co., 130 S.W.3d 181, 189 n.3 (Tex. App.—Houston [14th Dist.] 2003, pet. denied). Such a contractual obligation can arise through settlement. This interpretation is bolstered by the inclusion of “settlement amounts” in the list of payments included as damages. With those two misinterpretations clarified, the settlement payment’s inclusion in the policy becomes clear. The policy covers “Loss . . . resulting from an Entity Claim.” The demand letter that the Geibs’ attorney sent to HMI constitutes an Entity Claim because it is a “written demand for monetary damages or other civil non-monetary relief.” The HMI’s settlement payment constitutes a Loss because it is an amount that HMI is legally liable—through contract—to pay to the Geibs as a result of the demand letter. The fact that the Geibs never filed their threatened suit and that the limitations period had seemingly run does not change that. The policy does not require that the party suing the insured win a judgment.[4] Nor does it require that the insured meet a threshold likelihood of losing the threatened lawsuit before a settlement can be covered. The party defending the suit, threatened or filed, has the right to measure the legal risk it presents and decide whether to settle; that is why insurers that breach their duty to defend cannot challenge the reasonableness of the settlement amount. See Evanston Ins. Co. v. ATOFINA Petrochemicals, Inc., 256 S.W.3d 660, 670–74 (Tex. 2008). The fact that the statute of limitations, and not the merits, was the reason HMI was likely[5] to prevail does not change that basic tenet of insurance law. III. Twin City raises two alternative grounds supporting the summary judgment in its favor. First, it contends that the settlement between HMI and the Geibs was not the result of an adversarial process, so it has no duty to indemnify. Second, it contends that a policy exclusion applies. For differing reasons, neither supports the summary judgment.[6] A. Twin City’s theory that it has no duty to indemnify because the settlement was not the result of an adversarial process does not support the summary judgment for two reasons. First, it’s not the case that insurers, as a matter of law, have no duty to indemnify settlements that did not result from a fully adversarial process. Instead, such a showing only releases an insurer that breached its duty to defend from being fully bound by the settlement. See Hamel, 525 S.W.3d at 665. In other words, showing the settlement did not result from a fully adversarial process gives insurers the opportunity to contest the amount and validity of the settlement, but it does not give them a get-out-of-coverage free card. Second, HMI and the Geibs’ settlement was the result of a fully adversarial process. In determining whether the proceeding was adversarial, “the controlling factor is whether, at the time of the underlying trial or settlement, the insured bore an actual risk of liability for the damages awarded or agreed upon, or had some other meaningful incentive to ensure that the judgment or settlement accurately reflects the plaintiff’s damages and thus the defendant-insured’s covered liability loss.” Id. at 666. The possibility of being liable for damages or the settlement if the insurer does not ultimately cover it is an adequate incentive to make such a settlement adversarial. Id. (discussing ATOFINA, 256 S.W.3d at 673–74). Typically, cases in which that possibility is absent involve the insured assigning its rights against the insurer to the party suing it as the entirety of the settlement. But that’s not what happened here. HMI settled knowing that if it lost this suit, it would be on the hook to pay the settlement; that is enough to give it the proper incentive to reach a fair settlement. B. Twin City’s contention that a policy exclusion applies also does not support the summary judgment. The insurance policy excludes “Loss . . . in connection with any Claim based upon, arising from, or in any way related to any actual or alleged . . . rendering of, or failure to render, any services for or on behalf of others for a fee . . . .” Twin City contends that that exclusion removes HMI’s settlement payment from coverage because HMI regularly performed wire services for the Geibs for a fee, and the Geibs’ threatened negligence suit arose from a wire service. HMI admits that it provided wire transfer services to the Geibs as a matter of course but denies that it did so “for a fee.”[7] It has enough evidence that the wire transfer services were provided gratis to preclude summary judgment for Twin City. Specifically, HMI points to the Administrative Services Agreement between it and the Geibs, which lists the services HMI charged the Geibs for and does not mention wire transfers. HMI also points to its employee’s testimony that certain services were provided for free. That is, at the very least, enough to create a genuine dispute of material fact on the question.[8] We VACATE the summary judgment in favor of Twin City and REMAND for further proceedings consistent with this opinion. We place no conditions or limitations on what actions the district court should take on remand.