OP here with an update. As I said originally, the caller did identify themselves as "Detective ______" (I don't remember the name and I didn't write it down) of the Regional Auto Theft Task Force. But I had never heard of such a thing and I was wondering why his caller ID was blocked and the whole thing was very fishy and then the call was over.
I did talk to the SD Police and they just kid of shrugged; though they did say it was standard practice for Detectives to have caller-ID blocked on their cell phones. I haven't pursued it further.
The broader point though is that I don't see why people think Tesla Model S's are so secure and safe and worry-free in terms of theft.
Seems they're highly desirable cars just for parts alone. *Especially* now that the 21" wheels are what, $4500 for the set? Just taking the Tesla to a chop shop might be very lucrative.
Personally, I wish the car were more secure. I wish it had a startup PIN or something. At the very least, a PIN for making any settings like disabling the remote access! And I don't particularly like the fob thingie. Anyways, I'll prolly do a writeup on my observations of the car once I have had it for a while.