I don't think that is legitimate reasoning. People living under the constant threat of violence, even when they are not dodging militias and lynch mobs, are not living in peace.
Yes, but why is that? It's because we humans stress on hypotheticals (and unless something is actually happening at the moment, regardless of whether it's likely or even immenent, it is, for the moment, just a hypothetical).
Going back to the rabbit/owl analogy; the rabbit is under constant threat from any number of things that would like to eat him, but, unless he actually sees the owl's shadow, or catches it's scent, etc, as far as the rabbit's concerned, the owl isn't an issue (the leaves he's munching on are the issue at hand).
If we can suspend empathy for a moment for the sake of objectivity you can see that the only difference between the rabbit's situation and that of a human living in a war zone (for example) is what they each do with the time between violent events; the rabbit lives in the moment, we humans stress (fear, anger, outrage, hatred, grief...) over what just happened or what could happen next.
Not saying that isn't as it should be, just saying it goes a long way to explain the apparent lack of peace in the world, not just psychologically but pragmatically; our reality is disrupted by violence (even hypothetical violence) and we respond with more violence (including the violence going on in are heads as a result).