I see your point. I guess I just don't care about that potential distinction, just in that it was effective to me either way. Whether he happened to be nearby or whether he only came nearby because of it. One is more heroic than the other when it comes to motivation though. To me, both could easily fit Batman/Bruce. Given his actions in the rest of the film, I would lean towards agreeing with you that he only went nearby because he already knew about the destruction.