Either way, if the civilians are effective, we should still see the incidents that do run upon an armed civilian end in fewer deaths. I'm not sure that's the case, from the quick reading I've done.
I'd have to find the article I found about the 9 instances to see their detail.
I do suspect that the bad guy will always get a leg up and a few shots in before anybody on the planet could possibly stop him. Simply because unless I am parked in my car, see the bad guy walk from his car into the nail salon with 50 guns strapped on him, I'm not in position to start shooting first. And other than calling 911, I'm not sure what the best strategy would be. With a pistol, shooting a well armed guy across a parking lot seems risky (missing, return fire from a rifle, etc). Or do I get out, try to sneak up on him and cap him from close range?
So any first responder is responding to the attack that just started. Which means some folks are going to get hurt. Active shooter situations win initiative basically and get their surprise round.
There's also the usual excuse that attacks happen in no-gun zones like schools. Nobody in a school is supposed to have a gun. Which makes it easier to get your murder spree on before anybody with a gun can get to you (generally cops).
While I am for having the right to have a gun (I have some), I don't see them as being useful/applicable all the time. Bad guys will break into my house when I'm not home, so I can't shoot them then*. A home invasion will happen while I am going potty or watching TV and don't have a gun handy. Half the places don't allow guns, so my gun gets left in the car when something crazy happens (which is actually pretty rare anyway). Having had a friend who almost got carjacked at a stop light, probably the most likely time/place to keep a gun handy and have it be useful is in the car for when roadside crime happens or for entering/exiting the vehicle for parking lot robbery. It's why my wife got her CHL because employees where she worked were getting robbed in the parking lot.
*this happened to me last year.