Charge and bill are two separate things at a doctor's office. They may charge you for the specialist visits, but they may not bill you for it (after they received payment from insurance). They have a contract with the insurance companies. Generally speaking, if the benefit form from the insurance company states that patient responsibility is 0, then you shouldn't have to pay anything to the doctor's office.
You can require them to make a copy of the form they want you to sign. Read it at home carefully before you sign it.
