Other than the few having issues with the BD-Rom the only issues I've heard of are:
A) People set them vertical rather than horizontal, which it clearly says not to do anyway, and I doubt this would have anything to do with memory
B) People use the recently found combination to enable "dev" mode (or fall for the online prank that says dev mode offers backward compatibility). In the first case, MS has explicitly said not to do it as it isn't the only thing needed and can cause issues, and in the latter it is a hoax as dev mode does NOT offer backward compatibility. If he happens to have turned this on, then I suppose it could cause memory issues.
If either of those is not the case, I don't want a picture and I can't help. Does he have any other games? Does it happen in other games? Basically either get ahold of Activision/Infinity Ward if it is just their game, or get ahold of Xbox Support of it happens over time on any game.
Oooh.. one other one, did he go into settings and turn on the 'enable fast resume' for games (or something like that), which is flagged in the settings as a beta setting? Just remembered one other thread I read somewhere that suggested turning that off if it was on