In concurrence with the above post, it is not a viable argument to directly link violent TV shows directly with violence in people's behavior. Consider, for example, the Baby Boomer generation that grew up watching a plethora of war movies made after World War II in which they was a great deal of killing. Then, they watched hundreds of Westerns in which men were constantly kiling each other or slaughtering the Indians. When they were not watching these shows, the children were playing "cowboys and Indians" and had toy six-shooters, some of which fired caps that made realistic sounds.
Boxing was also a huge sport in the 1950s and 1960s, showing real-life violence. Nevertheless, the violent crimes during these times were not in the percentages that they are today. Perhaps, then, an examination of the many other factors in society should be examined, among them the subliminal ideas in the music to which youths listen. For, studies have proven that songs do, indeed, affect people. This is why so many patriotic songs were sung during the world wars, for instance.
If I understand this question correctly, you are asking if there is some other way to explain the greater degree of violence among adults who watched a lot of TV as kids. If so, there are at least two things to consider.
First, there is the possibility that there is something about people who are prone to violence and aggression that draws them to watching TV. In such a case, the TV watching would not be causing the violence. Instead, the violence and the TV watching would both be the effects of some personality trait.
Second, there is the possibility that the people who watched a lot of TV were different in some other way as well. It could be that people who watched a lot of TV had less interaction with their parents. Or it could be that they came from poorer households that placed less emphasis on education. In these cases, it could be that the other variable (parental attention, emphasis on education) is what really causes the violent behaviors in adults. It is very hard for researchers to control for these sorts of factors when doing studies of TV and aggression.