Had surgery to correct an underbite a few years ago after prepping for it with braces for years. For context, I was still young enough to be on my parents' insurance. The surgery involved moving my upper jaw forward and my lower jaw back because the underbite was so severe. The insurance denied the claim. My parents (I love them so much for this) decided beforehand that, if the claim and the appeal were denied, they would instead "gift" me the money out of their own retirement savings and have me pay for it. The procedure alone cost, I believe, $16k out of pocket. (I don't remember the specific reason why they gifted me the money instead of paying for it outright.)
It might be that you HAD to be the one to pay for it. When I hit a certain age, all the insurance cheques were made out to me, and I had to deposit them and transfer the money to my parents.
(Though this was insurance for therapy, so maybe it's different?)
Insurance wasn't involved when it came time to pay for the surgery. By then, they'd already denied the claim and the appeal, so they were paying completely out of pocket for the surgery.