What do you think the lesson was in your story, not that you are frustrated because people didn't understand?
The problem with responding with violence in kind is it feeds on itself. I can undestand your friend not liking someone calling his mother a bad name, but when he touched his friend, that legally constitues assault, and in turn the person struck him back.
Nothing of this is justified, neither name calling, invading someone's space, or counter-attacking.
But when your friend lost control and then took it upon himself to run after the other person, he also legally became the aggressor when he laid into him.
So people don't see the whole story and respond with their perceptions, right or wrong, because they only saw the final attack.
The issue isn't people's thoughts about your friend.
The issue is about the use of violence and each use stepping up the power.
At some point the law could get involved, and normally when they do so, they aren't intersted in the lead up details, only what they saw when they arrived. And unfortunately you're friends response does lead to the possiblity of the law dumping on him.
Seeking a better answer, for example not listening to mere words, even downright cruel and nasty ones, only leaves the one uttering them look like a fool, and keeps blood where it belongs.
Revenge is for bad movies, and only hurts everyone in life.
bushi no te isshinryu