I wonder if the "anything" in that phrase comes from people mishearing a common saying and eventually morphing it into the wrong words. "Violence doesn't solve ***everything***" would be a better, truthful statement. People say these things like "I could care less" and it doesn't make sense gramatically. You might also hear a basketball-american say "he din du nuffin", which is true if you logically follow the phrase, but you know what dey means.