People put down wrong, fake or stolen SSNs all the time and it’s not uncommon to see multiple SSN listed on RAP sheets.
The vetting process for issuing UPINs are based on fingerprints rather than just alphanumeric criteria. You get printed on blue (civil) print cards and your prints are run against the prints in the criminal indices. If your prints don’t match a prohibited person record you get a UPIN. The UPIN matches to your fingerprints like the FBI number of a RAP Sheet.
This. I had to get a UPIN about ten years ago when I was denied on a NICS check. Seems some dirtbag had - or just used - the same name and DOB that I have. I had to get fingerprinted again, send the cards in and wait. Current law in Louisiana is that one's CHL meets the requirement for a background check, so things go more quickly now.