I've met a few demented HR bimbys that would actually be dumb enough to send a letter like this. My faves were the ones that were trying to stamp out cursing in a blue collar production environment. As in: [censored]? As for legality of it, I think it basically comes down to it's their parking lot, they make the rules. A lot of companies will extend their "right to inspect" policy past your locker and backpack and in to your car trunk. I really doubt that last one would hold up in court but doesn't mean they don't try it.

Back in the 80s I lived in Bethlehem when the Bethlehem Steel was getting beaten down my asian companies dumping steel in the US. They came out without a policy of no foreign cars, especially japanese ones, in any of their parking lots. Ford and GM plants doing the same sorta thing wouldn't surprise me in the least.

In the late 90s I was driving a 20 yr old Chrysler with rotted out quarters and fading paint but at least all one color. I had a white collar gig doing high end telecom work at customer locations. Most didn't care what I drove, some kinda dug it, others got real uptight about it. The evil Vanguard Investment Group was the worst about it. They never actually said anything the car itself but every now and then one of the clowns would come hassle me about where it was parked. I kept asking ok, where should I park it. They kept saying all I can tell ya is ya can't park it where it is. From time to time I would intentionally put it in the visitor parking right in front of the main entrance just to be a dick about it. Now that I think about it, kinda surprised they didn't tow it.