I don't agree with it completely, but I do feel that video games can exacerbate preexisting mental health issues. I don't believe a person playing video games, let's say a 13-year-old boy, who is perfectly healthy, not depressed or stricken with anger issues, would turn around and go shoot up a school. That's simply not what happens. There has to be some sort of existing mental health issue for video games to truly be the reason why some people act violently.
There are also plenty of people who play video games, me being one of them, who--like Anonymoose said--can distinguish reality from fantasy. This can be an issue in younger children if the video games are not monitored for violent content and if they are left to play for hours on end, but not the sole purpose of violence. I believe that the content can be dangerous if not explained or regulated for younger children.
Overall, I would say that no, video games do not breed violence, but rather video games can make an existing mental health issue worse.