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It's not illegal to release that information, because your billing information is not covered by HIPAA when transferred within the holding entity for purposes of "billing information and payment activities." A doctor has the right to know and understanding billing options, as a means of deciding what actions they will take with the patient, be it treatment, future billing options, payment plans, etc.
So yes, the physician absolutely does have the right to that information and it is not legal protected from this type of disclosure to a covered entity (a treating physician).