It all comes down to the old causation vs. correlation thing. Violence-prone individuals gravitate towards violent video games, but the body of violent-video-game players is much, much larger than those violent individuals. I think this applies to other forms of violent media as well (movies/TV/music/etc.) Additionally, one might hypothesize that the very fact that a child is allowed to play such violent video games (or watch violent movies, listen to violent music, read/write/commit violent things without parental or professional intervention) could be a strong indicator of poor parental oversight.
I do think that violent games/media desensitize a person to violence, but I don't necessarily think that's in and of itself 'A Terrible Thing.' Flinching less at violence is a far cry from being mentally conditioned to commit it yourself. I think most serious research into the subject has consistently pointed in these directions, but popular perception takes it out of context and turns observations into judgements.
The problem with popular perception is the news media assumes desensitizing equates to some sort of unleashing of already-heightened violent tendencies or something. But I think even the handful of anecdotal media-hyped occurrences have borne these notions out as exaggerated and flawed once the dust has settled and the sensationalism succumbs to facts and reality.
We survive as a species because our internal mental process meshes well with external societal pressures. Human societies and then humanity itself would have died out a very long time ago if being surrounded by or even committing significant amounts of violence led to some irrevocable or permanent flipping of a violent switch in everyone, or a majority of people, or even a significant minority. People do break under very stressful situations, but their reaction has a lot more to do with their own personal, physical & cognitive development than the external stimulus.
