I've essentially come to the same conclusion as you, although more polemically: It is as misguided to say that violence in the media does not influence our choices as it is to say that guns don't kill people. But what has really struck me about Newtown is related to something I heard on the Freakonomics podcast: It's really hard to make our kids better than genetics dictate, but it's really easy to make them worse. Our children are influenced to the point that we provide them perspective.
I really appreciate the polemical angle, too. For one, guns clearly do kill a variety of animals limited only by the shooter’s imagination, ambition, and will. Sure, the shooter’s will is often primary (“often” because people are also accidentally killed by gunfire), but just as I cannot cook an egg without cooking equipment and methods, I cannot kill a person without killing equipment and methods. Where the will to cause death exists, efficient killing instruments necessarily multiply a person’s ability to kill. If we didn’t believe that, we wouldn’t seek to control the proliferation of nuclear weapons. Just ask an NRA member how many nations should have nukes.