Oh heck no.
I completely agree. I would call your insurance, the anesthesiologist, and the hospital. I had the same issue with my first. I expect when I go to an in network hospital, I will get in network doctors. It is not like you had a choice of doctors and where you supposed to ask what insurance he takes when he came into the room. I didn't get anywhere with anyone until I called the patient advocate at the hospital and then it mysteriously cleared up. Good luck!