Well, to be fair, they DO have their secret weapon of Batman in the movie (the last trailer really focuses on him as well). He's box office bullet proof, especially thanks to the Nolan movies that are still remembered fondly (and, hey, Batman's awesome regardless!). And Batman lives in a world of dark, it works for him.
More telling would have been Man of Steel 2 or any movie that doesn't have Batman in it to see people's reaction to a non-Batman darker movie. It's telling that Man of Steel 2 was sidelined for Batman's inclusion so quickly.