Sorry. I figured my "target audience" for the question would know...I didn't think about the rest of y'all ;)
CCW is a permit to carry a concealed weapon (it's known by different acronyms in different US states). Depending on the state, you need a permit to carry things like knives in addition to handguns.
In my state, I can legally act in defense of a third party. If, for instance, a family member, friend or complete stranger is being attacked by a group or a mugger with a weapon or whatever, I am legally in the clear if I use my concealed weapon in their defense. If the situation is life threatening (there are guidelines for this), I can act in another's defense just as I can act in defense of my own life.
First of all, you have to know that the 'scruffy attacker' is not, for instance, an undercover cop, or that the 'victim' is actually a victim. This is why you're usually better of just being a good witness and not intervening.
Once that's covered, if you actually do act (or, for that matter, if they are a witness[used here in the non-JW sense] to you acting in your *own* defense), it is possible that, once the sh*t has hit the fan and they're not in danger anymore (the bad guy runs off after he sees your gun or is on the ground bleeding or whatever), the victim that you've just saved (or the witness who saw you act in your own defense) can turn around and freak out on you for drawing, or even having, a gun. Even if you were completely justified, according to legal guidelines, statements that they make to the police can get you in serious trouble. Worst case, an anti-gun 'witness' can make it sound like you were in the wrong.
So, knowing that the Society's stance on armed self-defense is that it's wrong, a person might be taking a bigger risk coming to the aid of a JW than they would a member of the general public.
It's just sort of a philosophical conversation...