I don't know if this will help or not, but it is what I do know about.
When I lived there and needed surgery I did have some insurance, but it covered a percentage and many things were just not covered by my plan. When I knew I needed to go in I contacted and talked to the hospital directly and they indicated if I would pay some in advance they would reduce the amount I would ultimately owe, and they were very easy to work with on the payments. I've always tried to work with them up front, it is much easier than later.
A very popular court case shaped how medical bills were viewed and treated in Arizona- maybe 8 years ago - sorry don't remember the names... Anyhow, the provider decided to accept the insurance payment as the full payment, and not charge the patient their require portion. The insurance company declined to pay their billed portion, saying if the patient responsibility was "0" then the insurance responsibility was 80% or that, or "0". It went to court and the insurance company won. The court found that the way the insurance policy was written was it would pay 80% of the total patient responsibility of reasonable and customary charges. If the patient owed "0" then the insurance company did too.
All the knowledge an insurance geek can share!!! Let me know if I can help further, PM if you prefer...