do with the facility. Typically, the provider is an independent contractor or part of a group that isn't affiliated with the hospital.
Often, the hospital extends privileges to a physician to practice, but outside of that they have no control over the physician's billing.
The patient's insurance, the physician, and the patient are left to sort things out. If the physician is out of network the insurance also has no leverage with the physician, which leaves the physician and the patient to sort out the unpaid portion of the bill.
Just read about balance billing and it will make more sense.