Yes, paintballs can and will damage car paint. Besides the scratching or even chipping of the paint from the impact itself, if left on too long, or in hot weather, it can and will stain.
And even if it was 100% harmless to the car, it's still illegal. Shooting a car with a paintball gun is identical, from a legal standpoint, to spray-painting it or throwing rocks at it. It's vandalism, and it's illegal.
If you're working the counter and somebody asks you that kind of question, that's what you need to tell them. It's misdemeanor vandalism at best, and if you do more than $500 in damage (depending on local laws) it's a felony.
And if the car owner has to pay to have a door refinished, it'd go way past $500 in a big hurry.
At our local store, we actually stopped selling paintball gear, especially paintballs, except to known regulars, for the week leading up to Halloween, in order to help reduce vandalism. And more than a few times we helped the local police when something happened- most of the time it was telling them how to tell the difference between the paint we sold (mostly RP Scherer Premium Gold at the time) and the paint the local box store sold (cheap Brass Eagle.)