If you have surgery in a private operating room, there is often a flat fee for surgery. If your procedure is performed at a surgery center or hospital, they usually bill by the hour. That means the surgeon charges one fee, and the total price for surgery is basically an estimate based on how much time your surgeon thinks it will take. If it’s longer, there is sometimes a bill for additional operating room and anesthesia time.
I would ask the office if the charges are valid, and let them know that you didn’t think you’d be billed after surgery. They may be able to straighten out the charges or at least make sure the policy is more clear to future patients.