I've called my insurance company to check whether they'll cover certain medical procedures. And they'll actually play a recording before transferring your call - something like "Statements of coverage during this call are estimates, and are not actual guarantees of payment."
I also learned that they have a whole bureaucracy already in place for appealing of payments. (People whose job it is to field all the rejected and then appealed claims, and write multi-page letters explaining their reasoning...) So I took my complaint to my state's consumer complaints department. Let the two bureaucrats explain things to each other.
And in the end, the insurance company paid me.
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