But why would a patient want to prevent you to find its medical records?
There might be several reasons. Usually a patient goes to a clinic to get one of these services (the list might be not complete):
1) Medical verification
2) Medical treatment
3) Medication
4) Paying
5) Claiming Government Support for payment
6) Claiming Insurance Support for Payment
Here are now a few examples where the patient might like to hide his known identity:
1) Getting another verification (by another doctor perhaps) because he never is satisfied with the existing ones.
2) Getting more Medication than he needs, for selling or "helping" someone without required consultation
3) Getting a clean patient record concerning any invoices
Usually any way where is seen a real or supposed option to get something desired is used.
It would be naive to think that self produced social numbers without further identification really point to the right person and that they do it only once.
Therefore the usage of biometrics perhaps never allows to get the real data of a person but it grants that you always talk to the expected person.