I think the simplest explanation (assuming we accept the Gay Chad theory) is that Chad wasn't with the jocks when they beat up Troy. The only direct link is that Chad gives Sage the guitar, supposedly because he knows she wants to be able to play the guitar. But Sage wasn't there, she only knows that Chad gave her the guitar.
So it's possible Dawe was beating up Troy on his own (well, with a few other jock for support, of course). When he saw the guitar, he figured Chad could give it to Sage so he took it with him when he left. Chad wouldn't have any other use for it, so he why not give it to Sage?
There is another possibility, though. Perhaps Troy was kicked out of the jocks because he was caught doing something "gay" and Chad couldn't save him lest their relationship become public. So when the other jocks wanted to beat up Troy, Chad might have been roped into going with them to keep up the ruse. In this scenario, Chad might have seen the guitar as an excuse to end the beating and get the jocks out of there: he could say it's the perfect gift for Sage and they should leave before if breaks in the tussle, or something to that effect.
Neither explanation is flawless, but I think both are more likely than the Mel scenario.