Question about gap exceptions and balance billing

Hey all, gap exception related question for you all today. I had a medical procedure done that cost $2000 (making up that number). It was done by an out of network provider who told me the estimated out of pocket cost beforehand based on a conversation with my insurance. I paid that before the services were rendered (say it came out to $1000 when factoring in deductible and coinsurance) and largely am fine with it.

The provider, because they are out of network, applied for and received a gap exception with my insurance. This processed it at the in network rate, which my insurance says they are bound by because of the waiver they got. All in, they are paying the provider $700 (again, number for example purposes).

The provider is now trying to bill me the extra $300, saying they have a contract with me and can do that. My insurance company is saying when they agreed to the in network waiver, they agreed to accept the cost my insurance company paid, plus my deductible, and can’t bill me the rest. It’s not a surprise bill, but a balance bill.

Who is right? There’s no state law on balance billing and I’m not sure in which direction this should go, but I’m not sure if I’m responsible for the balance in this situation.