I think it completely depends on the child AND the game.
My son is not allowed to play every E game (some are absolutely AWFUL), and he IS allowed to play some M games. T games tend to be the worst overall IMHO... because they tend to be gratuitous everything, shoddily engineered, and badly thought out as a rule. Many M games, on the other hand, are multimillion dollar projects full of great depth and subtlety.
We go on a game by game basis. Just as an example ds8 IS allowed to play all 6 of the HALO series, and the old WWII version of Call of Duty... but NOT Call of Duty World At War or CoD Black Ops.
When kiddo's friends are playing with him we have a lowest common denominator rule. AKA, he's only allowed to play games with his friends that their parents have given permission for, and vice versa. People have different rules, and that's just the way it goes. We make sure that NO ONE is breaking their parents rules... whether it's his friends or him.