I'd like to see links to studies that prove there is no link between video games and violence. They are incredibly difficult to carry out.
Firstly, who is going to put their child forward for participation in a study that will expose them to even potentially dangerous material? Even if parents did want to co-operate, research would have to go before an ethics committee, and they are (understandably) very tight on anything involving children.
Secondly, how do the researchers screen out other influences, to be sure that it is games, and not other things that have caused any violence that they find?
Thirdly, children who have never played games are relatively rare, so who will form a control group, and how typical of their peer group are they likely to be?
Fourthly, studies take time, and ones looking to show cause and affect are usually longitudinal. Games evolve all the time, so those being played at the start of a study are likely to be out of date by the end, so results become invalid.
To summarise, finding correlation in topics like this is relatively easy, eg that X% of children who play games commit violent crimes - more general findings such as 'become violent', or 'carry out violent acts' are based on subjective definitions of what is meant by 'violence'; but finding causation is much more difficult, as both control groups and willing participants are hard to find, and as games technology is fast-moving, studies can be out of date before they are published.
Studies into more general impact of the media (eg TV, film and so on) tend to show that violent children (and adults) have usually watched more violent media, but not that more consumers of violent media have become violent than not. It's all very inconclusive. I haven't seen any recent studies about games, but I would be interested to see the methodology as much as the results.