Yeah, as I wrote originally, this nagging idea re: violence first started when I was reading through B2 and preparing it for kids.
So, let me continue from the perspective of my experience - since it was a recent one in which I actively questioned the tolerances for many things in my game and presentation...
At the root, we view some violence as okay, because we still live in a world in which violence is occasionally necessary. There are still (entirely human) monsters among us, and sometimes we are not left with non-violent alternatives for dealing with them.
My 13-year-old players knew this, so I could use violence in my game to that extent. There could be foes in my game who were willing to do harm in order to achieve their ends, and the players could oppose them and use violence to do it. That would be okay, as they are prepared for it.
What wasn't going to be okay?
1) Explicit graphic brutality. Yes, it exists in the world too, but my 13-year-olds were not yet versed in what that really means, and it was not my place to introduce them to the idea and help them integrate that understanding.
2) The PCs as the bad guys. While it was okay to allow the PCs to take a certain glee from exacting a sort of rough justice, taking glee in getting what they want through violence was not going to fly - much for the same reason as (1), because to do that right I'd have to make it clear what kind of consequences that has - and 13-year-olds are not yet ready to understand the depths of those consequences. Thankfully, the kids showed no desire to be bad guys, even when the opportunity was easily available.