That's not a simple explanation, it's a convoluted one. If anything in your scenario Chad should be more aware he's cheating on Sage, since he's actively trying to hide whatever he's doing from her specifically.
Chad says he isn't cheating, no riders about with a girl in his statement. The simple explanation is either he isn't cheating with anyone or he's lying & is cheating with another woman.
If Chad isn't cheating then the problem is squaring the previous evidence: in the absence of any clues it's unknowable at this stage. I'm fine with waiting to find out rather than inventing explanations. ¯\_(ツ)_/¯
If Chad's cheating with a woman, I can think of lots of other reasons to keep it under the radar: she's married, she's faculty, she's friend/family of Sage etc. All fit the available evidence better than Chad is gay. All of them are still baseless speculation however, so pointless.
Depends, if you knew of and accepted your partners screwing around then obviously that's not cheating, that's an open relationship of some variety when there's mutual agreement. Pretty sure Sage didn't give Chad that leeway, so pitchforks for any cheating bitches she can track down (if they even exist).