When correlations are very hard to find, that's a sign they don't exist.
Science can't disprove things, it can only show if things are statistically significant correlated. This means that, for instance, it is impossible to prove that a substance is absolutely not cancerogenous, or that compter games absolutely do not cause violent behavior. It is easy to show strong correlations (for instance, that smoking correlates with cancer, or that driving drunk correlates with getting in to accidents), but as correlation gets weaker, it gets progressively more difficult.
Any situation where you have many studies which more or less randomly (or, as in the case of fictional violence vs real violence, tendentiously) get completely different results regarding whether two things are correlated, you should suspect that in reality the correlation is extremely weak or non-existent.
As for badly/tendentiously designed: my favorite "fictional violence causes real violence" study had a toddler placed for 20 minutes alone in an empty room with nothing but a doll, a plastic toy hammer, and a TV showing a cartoon in which one character hit another with a hammer. If, at any point, the toddler put any part of the hammer in contact with the doll, it was considered to have been inspired by the cartoon to hit the doll with the hammer. I'm sure it comes as a surprise that they found a correlation between fictional and real violence.