Keeping adult child on parent's health insurance

If you think the provider is wrong and they persist call the billing department and tell them you will be calling your insurance company and referring it to the “insurance fraud/balance billing division for investigation”
Then call your insurance company and do it!
It’s amazing how quickly that can get results. I had to do that with an issue I fought for 9-12 months. After I did that the provider called that afternoon and said my account was zeroed out.