Well, it does explain, however, why the Joker would allow such a lame tactic as unmasking to work, because he's wearing yet another mask(my that must get hot; ever try to breathe in just one?) and because it gives him a chance to cause some chaos. And get a compliment from his darling Batman.
Because had I been this "John Dough," I'd have simply said I was Batman, that the other man was an imposter, and as they're both masked maybe he should take his off. I mean, think about it.