Some things wear down, some things break with a snap (or a loud bang) all of a sudden. I have no idea whether your thermostat is stuck or not, but I have to tell you that while I have heard of lots of head gaskets blowing when engines overheat, I don't recall hearing of radiators springing a leak because of a stuck thermostat. Still, I am no expert in the subject, but it does seem to me that such leakage is suspect.
That being said, one half of making a profit in the insurance business lies in finding reasons to deny claims. Keep on it, don't give up.
In my youth, I was in an accident that resulted in some medical costs. After my health insurance denied the claim and appeals several times because in their own words "my accident wasn't an accident," I found myself asking the CEO of that insurance company to justify to the State Insurance Commissioner the accusation that I went out and hurt myself on purpose. That proved to be the turning point. Keep on the case, and best of luck finding the argument needed to resolve the issue. And the person to whom to make that argument.