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.