It does seem to me you could have saved yourself alot of hassle by saying "it's the black acura" or whatever it was you were driving.
Why try to swim upstream for no reason at all?
You got your car back. OK, you were made late. But you also kind of brought that on yourself.
The guy was just attempting to do his job. I agree, that would annoy me also if I were eating my burger or whatever, and have to spit out which car was mine. But, I don't really know the situation. It sounds like there is a parking issue wherever this is. And they are attempting to fix that situation.
Overall, there are large problems in life to concern yourself with. You have your car back. Next time, just tell the guy what car you are driving. You might even get to know the guy if you go to that fast food place enough times. It's usually easier to make friends with people like that, than to fight with them.