About 10 years ago I was shopping for a new car.  I went to a Ford dealer and did a test drive on a small car.  The radio had a removable face plate.  The salesman wouldn't put it on for the test drive.  So long Ford!  Bought European.  I hate dealing with all car salesmen.
As far as your SS#, that should only be needed for credit. 
I don't think the real "boss" knows what is going on.  Either that or just stupid.  You would think they would want to sell the car.  Sounds like they may run a credit check on everybody, but you were paying cash.  Weird.