Really important similarity to cops is that car sales people try really hard to control the physical space you are in. Can be simple, like, offering coffee, through shady, like taking your license on some pretext, to games like "wait here while I get the manager". The point is to lock you in a space and control the pacing and narrative.

This is why if you detect any nonsense like this, you should always remember that at any time in a car buying transaction, you can just walk.