Oddly enough it doesn't. For example, you can perform a credit check via this API using only a name + address:

http://www.meridianlink.com/creditAPI.asp

I have personally used this API, and it works.

SSN data isn't flawless. My brother and I somehow had the same SSN until I was in my teens (right as I started working but before he did so thankfully it wasn't too difficult to fix).

Doesn't matter. The credit bureaus mix people up all of the time, particularly if you shared a name and street in the past.

My wife and mother in law share a first name. And a middle name that varies by one letter. (Ie. Mary Ann and Mary Beth) credit reports routinely mix them up.

When I was in school in 1996, a collector managed to get a business debt of my grandfather (who shared a name and died in 1986) attached to me.