In the days before I carried, I had to intervene in a few scenarios. Two involved women being assaulted by men, and a third involved a friend (130lbs and asthmatic) having his head beaten into the ground by a 250lb football team center, whom my friend had reprimanded at work.
The first man vs woman turned out to be a domestic, although it had looked to me like a mugging at first. The guy and I squared off, but the woman talked things down... as I realized she was behind me, and I was very unhappy.
In the second instance, my ex-wife saw what was happening, and responded before I even realized the problem was occurring. I immediately followed her; the guy left; we took the woman to her relative's home. But that, too, was a domestic, just out in town.
In the third instance, I had seen the fight from its inception, knew the big guy was in the wrong, but was putting myself at some degree of risk. My small friend had chosen to fight back, instead of running away, because he was convinced the guy would simply follow him home and do a real number on him, when no witnesses were present. I ended up having to pin the football player, using a modified double armbar which put all his body weight over his head and neck, and held him there until the police arrived. Luckily for me, witness statements corroborated that I only intervened when the guy started bouncing my friend's head off the pavement, and then I only used necessary force to restrain him.
Football player got arrested, and I was bidden a good evening.
Where am I going with all this?
1) I don't think I'm Captain America, and I don't go looking for bad guys. OTOH, I would have a very hard time looking in the mirror if I did not take some sort of action, and allowed a woman to be beaten, or a friend to suffer a TBI.
2) While carrying makes me a bit more cautious and circumspect, I'm still not wired to stand by and do nothing. I would do my best to understand what was happening, but I would not (based on my experiences with such things, or for that matter with dog attacks, house fires, and near drownings) just walk off. Not only would I be unable to live with myself, but I'd disappoint my mother, who did not raise me to leave problems to somebody else. For that matter, the Navy didn't train me to leave the sticky problems for some other guy.
3) If some posters think that attitude makes me a vigilante, then we will have to disagree about what vigilantism is.