Here are some of my thoughts on this. It feels a little unorganized and unfocused, but see what you think:
First off, I don't take Whedon's comment as a singular idea. He says both "Batman gets short shrift" and "It’s not about Batman." I only agree with the first statement. Batman gets the "short shrift" because the major decisions in the film are split between multiple characters, and at times completely divorced from Batman. Batman is present in so many scenes, but too many of the film's critical decisions aren't made by Batman. I'm a proponent that the "main character" status is more sided with Harvey Dent and the citizens of Gotham than it is with Batman. Their decisions ultimately have a large thematic and narrative impact on Batman, but he's too often the spectator for much of the action (though that becomes more of a problem as the film goes on). So if there's any place where The Dark Knight begins to falter, it's the second half. The film drifts away from any notion of a strong, main character to anchor the story. Though there was plenty of talk (even by Nolan) that Harvey Dent is the backbone of the film, I'm not sure that's even entirely true -- or successful. Harvey Dent has what seems like a fuller arc, but it's slightly ruined by the way he's presented in the third act. His "transformation" into Two Face feels a little false, making it difficult to really put much weight behind him. More importantly, his plot of killing those responsible for Rachel's death is almost entirely separate from the main narrative of the ferry boats and hostages...he somewhat loses status as the main character at this point when the film puts so much focus on the ferry boat conflit. And that conflict, unfortunately, has little to do with our main characters. Neither Batman nor any of the main characters have decisive power in those scenes. Focus shifts to random Gotham citizens. For the third act, they essentially become the main characters. Though their ultimate decision has a large impact on Bruce's arc in the film, Bruce has no part in their decision making.
If anyone has seen Little Miss Sunshine, there may be a great way to tie this together. Olive more immediately feels like the main character in the film. It's ostensibly about her strong desire to win this pageant. But the main character in the film is actually Richard. Richard has to make the decisions that ultimately affect whether Olive can even be present at the pageant. Decisions that will decide whether or not the family will be held together. The Dark Knight ends with Batman taking the blame for Dent's murders in what could have been a strong attempt to round out the film as being "about" Bruce. But since I still haven't heard a compelling reason why Batman had to take the blame, it just doesn't work for me.