Whether he was armed, or unarmed would not have changed the scenario for the better either. He was not hurt, he only had his car stolen. If he was armed, it would have only made the situation worse, and potentially deadly.
Deadly to the criminal, hopefully.
Seriously, though, I agree that being armed in this case probably wouldn't have helped. If someone already has the drop on you, all they have to do is pull the trigger. You, on the other hand, would have to pull your gun, drop the safety and take aim before you can fire. Action beats reaction (unless you happen to have superhuman reflexes).
And if a BG sees you pulling your piece, they would be much more likely to shoot - after all, they have to defend themselves as well.