Since some people have questioned the fake batman idea. In Batman # 2, this did in fact occur, where an additional Batman was in Gotham, the fake appeared good but ultimately stepped over the line by killing cops, etc.
I assume, since this is also a Joker story and directly follows the first issue of Batman where the Joker appears that it is part of the basis of this film. So the idea is at least grounded in comics. It may or may not ultimately play out like in the comics, in the comics it was the organized crime not the freaks who had actually help create the fake batman to draw attention away from their crimes.