There are two points to this issue. First point is that there are nutcases in every fanbase, no exceptions. The second point though is that while each fanbase has their share of robbers, psychos, 85 year old women in wheelchairs who scream profanities at all the little children, etc., the crimes that those people commit don't seem to be related to the media that they are a fanbase of. For example, there may be someone who is a huge Mario fan who goes out and lights houses on fire or steals cars, but you never here anything in the news of a Mario fan going to rob someone just cause they HAD to play Super Mario World 27.
So my theory is this: the fanbase is no more unstable than any other fanbase out there. However, it seems that the instability of said people ends up targeting the games themselves instead of random crimes. Maybe because of marketing, maybe because they need to make sure they get good so they don't get heckled by the thousands of 7-12 year old kids who play the game, or maybe it's just because the CoD violence incites violence within them, I have no way of knowing. There is a statistic here and something about all this is throwing me a disturbance in the Force though, but whether this continues, improves, or nosedives has yet to be seen.