A practical question for your brother - If he's approaching a scene where there is a gun battle between the hypothetical competent law-abiding citizen and the active shooter bad guy, how does he know which is which?
Well, he has two options then:
1) Let the firefight play out until he knows which party is the original aggressor (ie, the Bad Guy). If one party is victorious in the firefight but then continues to shoot non-combatants, then he knows who the Bad Guys are. However, if the victorious party stops shooting after the firefight, the police order them to the ground and sort out the situation, determining eventually that they're the Good Guys.
2) Shoot everyone with a gun. This is bad news for the legally armed person, but is a known and accepted risk among concealed carriers (source: I am one, and I know many who are; we understand we could be mistaken for bad guys in this kind of situation, and accept that risk if we choose to engage the Bad Guy).
Either situation is a happier outcome for the innocent noncombatants than just hunkering down and dying en masse until the police arrive.
Now, collateral damage is always more of a risk with more combatants, especially with concealed carriers who don't keep up on their tactical training. However, I suspect that the overall damage is still lower than just letting the killer keep shooting at defenseless people, especially since most people tend to either run or take cover when gun fire starts, meaning there won't be too many people in the line of fire for very long except in very crowded places, and so the overall casualties will still be lower.