when Dent claimed to be Batman when Wayne didn't come forward, Wayne just let him take the fall, which was foolish and cowardly. A real hero wouldn't do that.

With this statement, I disagree. By doing this Dent was saying to the real Batman "Look, I don't know or care who you are, but I know you're in the room right now, and if you think you are going to get out of dealing with the Joker by handing yourself in, you have another thing coming, because I'm going to deprive you of that option."

Wayne's silence was thus a "Yes, Sir."