What the hell does a GAME have to do with shooting a bunch of people? I've been playing these kinds of games since I was 2 years old (space invaders is a sweet game) and the only thing they make me want to do is play more of them.
Besides anyone who has shot a gun in real life will tell you that even as hard as these game people try shooting a gun in the game is NOTHING like shooting one in real life. To that end a lot of people watch football but I haven't heard of people running around and tackling random people and than everyone blaming football for it. Your first point was correct these are people with mental issues plain and simple and no video game or football game increases nor decreases the likelihood that they will end up doing something depraved and gross.