I'm not going to get into whether I agree with the media violence link to real life violence, but I want to point out it's not simple. My DH and I were once on very opposite sides of the fence, I originally came from a ECE and Waldorf early childhood perspective, and DH was once a computer engineer and video game beta tester (he's a nurse, now) so very opposite! What we both found researching this matter, was that it's hard to sort out variables. Parents who don't provide rules and structure with television viewing may provide less general structure, too, which is also a risk factor in violent behavior. People who are already predisposed to violence may prefer violent programming. The TV itself may lead to some children spending less social time, regardless of content. OTOH, the risk in a growing brain may be greater. And whether we now have increased violence now in a day and age of increased video violence is even disputable, violent crime has actually gone down in much of North America, and there are differences in the rates of reporting violent crime that could skew crime statistics, too. It goes on and on, with studies both for and against, and it's not simple. Both DH and I fall more in the middle, now, especially now that our two older children are preteens and we've experienced seeing them grow into their own people as the outside world is increasingly more a part of their lives. Here is a link from a media awareness website, with some statements from both points of view:
Also, I think it's worth being aware that the news can be one of the worse sources of media violence out there. It is obviously not fake, and violence is over reported compared to positive news. It can give the impression that the world is way more dangerous than it is, and fear can breed aggression as much as desensitization. And, whether an adult watches the movie with the child may make a difference, as they can explain and contextualize what the children are seeing. I think it's a good habit to be aware of what your children watch even if the material is supposed to be child friendly.
On a practical note, the TV program "Dr Who" was originally meant to be a preteen friendly horror/Sci-fi series, and there isn't anything obviously gory or bloody, although there is death and fear. This is the middle ground we've used with our own kids, I think it's still a step up from the really gross horror movies, but they still find it fun to watch with friends over. Either DH or I or both of us usually sit down to watch with them (always if we haven't seen the episode yet, because we also have a 7 year old who definitely can't handle any visual violence) and eat popcorn. Sometimes we have some pretty neat discussions, later, too.