I don't believe that. I think that the calculus of whether to attack someone skips the "is the victim armed?" question. You just make sure to bring overwhelming force, e.g. bring a gun to a (probable) gun fight or a knife to a fist fight.
But what do I know. I'm just an European wuss, who has fire a handgun exactly once.
The deal is if you carry, which I did for years, you have to maintain above normal situational awareness. You have to be able to get space. Cops can do this because they arrive after the fact and get to enter the situation with the appropriate threat posture. If I have a gun and I get into an altercation the moment i'm in physical contact with the other person the gun doesn't matter. The long and the short of it is if you can be prepared and have "the drop" on someone a gun is a great way to protect yourself. That is why I feel the shotgun at home is a good idea concealed carry an overall liability.
Source. I lived in the 14th most dangerous neighborhood in the us for 15 years and carried a gun most of the time.