I'm trying to point out the slippery slope of adults offering this kind of arguments to children. I wouldn't tell it to my kid because I feel it would be the wrong thing to say: "Here's a piece of advice that might work in the schoolyard, but it's wrong in life overall."
Except that it is definitely NOT wrong in life overall.
There is a big difference between saying "violence doesn't solve anything" and saying that "violence solves everything".
There are many situations in which a person needs to defend themselves, and reacting to physical violence with a physical response is the right thing to do. Just because this gets out of hand because some people take it too far doesn't mean that all physical responses are wrong.
So if one of your closest loved ones were threatened by a violent criminal (in a home invasion, for example), you would actually allow yourself and/or your loved one to die rather than commit an act of violence that eliminated the threat?