Cool idea. YMMV with this, though. The government accidentally assigned me someone else's SSN (had the same first/last name as me and was born in the same hospital) and it took about 2 years to rectify.
The first and last name may be a coincidence, but depending on how old you are the "same hospital" is likely not. SSNs are generated based partially on geographical area, so if that's the only or the biggest hospital in the area, the likelihood of getting a number from the same hospital is substantially higher.
If you have someone's SSN, you can pretty easily deduce what city they were born in unless they are very young (they switched this process recently).
Presumably, sho'he requested a credit report to verify success and saw a lifetime of someone else's credit interactions (different car, mortgage, credit cards). <edit for irreverent trailer : https://www.youtube.com/watch?v=OnouJoQs52c />
If you have someone's SSN, you can pretty easily deduce what city they were born in unless they are very young (they switched this process recently).