Once the athleete/nerd stratification has been established, it may create bullying incentives for those who are physically stronger than the nerds, but not part of the elite athlete circle. Such individuals will want to assert superiority to the nerds to at least confirm their middle-rank status if they can't achieve the top one, and bullying seems like a straightforward strategy.

I didn't go through the American school system either but your theory seems to match with general observable tendencies. Bullying and crude social aggression isn't an indicator of high status so much as an indicator of 'medium high status that requires effort to maintain'. This is why I make sure I never work for an insecure boss.