I encountered an almost identical scenario.

It is a ranch style property, both units mirror image each other and are identical in size.

So I wouldn't have even considered this applicant.Also, keep in mind that while it's possible the applicant is concerned about identity theft, it's just as likely (if not more) that they're not providing you their SSN because they're hiding something (i.e. bad credit, collection accounts, evictions, etc) and they don't want you to find out.  

Looks like there are a bunch of identical properties right there.

So a broker buying a house without representation is charged identically to a non broker who is represented by a buyer’s agent?

I used to have a couple of identical looking locks and would just switch the lock and rotate them as tenants moved out. 

Idem sonans is a legal doctrine whereby a person's identity is presumed known despite the misspelling of his or her name.

Hangs upClearly identity theft in action.

So, you either had to come up with $21K or $49K.Either way, there's a new loan product out there that will enable you to do an identical project for as little as 10% down on the acquisition and 100% finance the reno costs. 

If the broker created an LLC to mask his identity, that should have exposed it so if it didn't, maybe someone inside is in on it?