You'd need to ask the question; is it because they're going to private schools or is it because rich people are more likely to try shit because they know they'll get away with it?
I'd say it is, but it's mixed with Public School types see it as a joke in the first place. There's a different perception of doing antisocial stuff which relates to your class. Acting the prick if you're rich is just the boys being inveterate scamps. Acting the prick if you're poor is further proof that poor people are cunts. Everyone is clear on this.
There's an additional upstream element of the getting caught and getting away with it or not part. It's the perception of the action itself is funny or not serious if upper class people do it, and vice versa. Additionally yes, they're likely going to get away with it, if they're caught. But that's after the moment, that's in slightly a different context.
Maybe.