Rule #1 of health insurance coverage -- send all bills to the insurance company first, let them tell you what they cover and what is your responsibility, not the doctors billing staff. I still have times when the doctors staff tries to get something out of me like, 'we know this is the amount not covered.' I respond that they should send the bill to the insurance company or bill me and I will send it. I don't pay anything until I see an EOB (explanation of benefits) that shows: billed amount, adjusted amount, amount paid, and amount you may owe.(and other stuff like deductible remaining, out of pocket max, etc.)
I had one bill after my surgery from some doctor that I did not know for a few hundred bucks. My EOB showed it as something like 'coded procedure not covered.' I figured the doc put the wrong code in and wasn't getting paid because of this. I kept forwarding the bills to the insurance company and they responded accordingly. Eventually the doctors billing staff fixed their error and got paid. (not from me).
Like what was said previously, if you are using an in-network doctor or facility they are bound to accept the adjusted amounts set by the plan. If it is out-of-network remember your out-of-pocket maximum may be different than for in-network.
Good luck
Neal