Violence in media is different then violence in real life, usually. Violence in media is usually overplayed and exotic, intentionally made over the top so we can relax a little. That, accompanied by the understanding that what we're seeing is not real. Watching The Bride from Kill Bill backflip and chop off a gangsters arm, accompanied by a ridiculous shower of bright red blood shouldn't be offensive, because it's so ludicrous that it can't be taken seriously. And when violence is portrayed more realistically in media, it's usually designed specifically to give us a sick, unpleasant feeling. For example, the D-Day scene from Saving Private Ryan, or to use a more recent example that's been a big topic this year, a couple scenes in Spec Ops: The Line.
I've been exposed to a lot of violent media from a very young age, but I've always been able to make the distinction. I'm still offput and sickened when witnessing real violence, not even firsthand, i.e., some of the pictures we stumbled across when studying the Holocaust in school.
Violent media CAN lead to violence in people who are unstable, and can't tell the difference between reality and fiction, but that doesn't mean that everyone who is exposed to it will react the same.