Change in patient identifier

this is the scenario:
in staging I have a patient table with identifier MRN. Also have an admissions table with account Number and MRN.
in the warehouse, I have a patient dimension with MRN and an admission fact table with account Number.

Issue:
patient comes into staging with incorrect MRN, thus it is loaded, along with demographics to the Patient_D and the fact table is loaded with the correct account number but incorrect patient key.

the error is corrected, and into staging comes the same patient with a new MRN and the admission data with the correct account number, MRN.

now to fix the previously, incorrectly entered fact.
I can add the patient again to the patient_D, but unless I try some algorithm to match the previous record (match on name, DOB, SSN....this is not foolproof at all), I can't 100% identify it to give it a new version number, or to update it. So is it best just to add the new record (patient is entered twice) and just correct the admission fact record with an update to the correct MRN. The problem is that the patient_d has duplicates in it and then reporting on patient volumes would have to go through the account_fact table at all times. Is this the best way to go with this?
thanks
Jeff

Isn't there a claim or admissions document number associated with the fact?

there's an account number in the admission_f