Psychologists explore public policy and effects of media violence on children
Although hundreds of studies link media violence to aggression in children and adolescents, most public policy attempts to reduce children's media violence exposure in the U.S. have failed.[..]
There are also reasons why the public hasn't called for more preventative measures.
"One reason is what's called 'the third-person effect' -- that it's a lot easier to notice these types of effects on other people rather than in ourselves and those closest to us. So most parents don't think media violence affects their kids," Gentile said. "That's partly because media violence effects accumulate slowly and people aren't good at detecting small changes -- even though those changes could be big by the end.
"Another reason is that the news media primarily focus on violent media effects in terms of atrocities like Columbine," Anderson said. "This confusion about equating media violence with extreme atrocities allows people to think that there are no effects on them because we all know that we've watched lots of media violence and never gone on a shooting rampage, but that's not where we should look for the effects. The effects are more subtle. In order to do something seriously violent, one must have multiple risk factors for aggression – media violence is only one risk factor, and it's not the largest one. It's also not the smallest."
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I think the above points as reported in the news release describe some of the opposition to the study in the OP very well. Furthermore, the article continues that public policy with regards to media violence usually follows a major tragedy, resulting in a knee-jerk type of response. We all know that's not a very good way to go about things.
Here's the link to the abstract for the actual paper: Public Policy and the Effects of Media Violence on Children
Unfortunately, access to the full paper requires a (paid) subscription.

