I agree with this. The majority of people who conduct these studies and find that video games "make people more violent" are generally trying to prove that they do. Probably everyone can attest to at least one friend they know that acts more aggressive while playing games, but definitely not after. My own brother swears like a sailor when he plays flash games about amoebas and Tetris and the like; it's more of a competitive aggression than a response to violence.
Also, in terms of desensitizing, it's more likely that the news desensitizes people than violent video games. Nobody even flinches nowadays when they hear about another car bomb or some other terrorist attack. Killings happen daily; it's a pretty well-known fact. When the news constantly report it, people stop caring. Playing Halo 3 or COD: Modern Warfare 2 aren't what make people yawn when they hear about the latest tragedy befalling people in Darfur, Rwanda, etc. It's the fact that when news stations constantly report such things, they simply become... expected.