I think that it is fair to assume that if a crime is going to happen, and the intended victim (or a bystander) shows a gun, then the crime probably won't take place. However, I also would think that the incident would be reported to police.
This may just be my own bias, but if someone is trying to rob me and some dude walks up and points a gun at the would-be mugger, who then runs off, I would call the cops. I think most people would do that as well, but maybe I'm just not desensitized enough to guns. Maybe other people think that someone pulling a gun in public is a common enough occurrence that it doesn't warrant police involvement. I don't agree, but I don't know.
However, my main stance is that I don't agree that more guns is the solution to anything. The reason that concealed carry works (as in the OPs story), is because both parties don't have access to a weapon. The more weapons that are put onto the streets, in the good guy's and the bad guy's hands, then the more escalation which will occur.
While in the short term, you might feel better because you're more likely to have a gun than the bad guy, in the long run, you're just inflating the gun numbers and forcing more criminals to get guns in order for them to engage in their enterprise.
Buying a gun does nothing to stop the number of criminals on the streets, it doesn't treat that, it just provides a temporary stopgap to the problem of crime.
