Am I Wrong?

Someone, please tell me! I recently had a procedure in a facility where you go for a day. Insurance was supposed to cover so much for the facility and the doctor and I was to cover the co-pay, which I did before they took me into the back. When I left there I thought it was a done deal, but then soon began getting bills for this and that that wasn't covered by insurance. Maybe I'm wrong but in the old days didn't you pay one bill and everyone got paid from that? Now it seems everyone who even touches you sends their own separate bill.