Well, here is a story I heard (central Europe).

Parents did not want the baby, so they left it at the door step, date of birth was not known, so some was assigned and used in some legal documents. Later, original parents changed their minds, real date of birth became known.

(For sanity sake, I would just say choose one or flip a coin and be done with it, but at the same time I could imagine that some layer could take my sanity into account)

The DoB may change (per law, not the real), for example refugees without travel documents often get assigned Jan 01.

A person can't, but there can be multiple people with the exact same name, with different birthdays (or even the same!) so DoB isn't guarantee to be unique without some other identifier.

Ah, that makes sense. So the DB likely assigned the incidents to multiple different persons with the same name and not a single person.