Sure, you 'could have' shown him proof that the car was yours. You also could have put on a Spider-Man costume and run around the parking lot flapping your arms like a chicken and singing Twinkle Twinkle Little Star. The point is that it wasn't remotely within his rights to demand either of you, since you were a complete stranger to him, the car wasn't his, and he literally didn't have a single piece of evidence to suggest that anything inappropriate - much less anything illegal - was going on.