Yeah, I was about to say something. My nozzles are exposed on my undercarriage. People drive over them sometimes. Its kind of like driving over gravel. I can't imagine a car that would lose a tire driving over a piece of gravel. I have never had an issue with that.
If it was somewhere else in your wash, yes, you should probably pay for it but at a prorated rate! Stick them a little bit so that they are mad enough not to come back but not mad enough to bad mouth your wash all over town. I personally don't want people at my wash who are such poor drivers that they cannot drive through an automatic wash. My opening is 12' and I have had people hit both the entrance and the exit with their cars.