Does Medicare have records of all item numbers billed for private patients in public hospitals? What if the patient was first seen as a public patient?

If a patient is admitted to a public hospital but chooses to come in as a private patient, the specialist will submit an invoice to the private fund. Will Medicare have a record of all item numbers billed? like 110 and subsequent 116s? The follow up visit as an outpatient should then not be 110 as Medicare already has a record of a 110 and will allow 116 to be charged? I understand that for a public patient in a public hospital, no item number is generated and Medicare has no record of any during an admission?