I'm replying strictly because you have none, and I usually lurk. This one is too interesting to let go.
I am highly intelligent, and went to public school (I likely could have used a private school or otherwise if it was anywhere near my parents means). Yes, shenanigans go on there. You don't have to be a part of it though - it really usually is a small group of those out to just break the rules. It's not that crazy, I often befriended such types to keep from getting bulllied (verbally was the worst part, I'm quite capable of the physical but it should really not come to that). It's not the outlaw country you're portraying, though I can see how you would get that from a private school POV.
It's funny to watch private school types melt when presented with real life problems or someone thinking irrationally.