To me, this is all easily explained by the fact that Batman is more than just a man, but a symbol. Symbols can do things people can't. They can hold meaning even in the absence of the people who created them- a key point in the whole trilogy. That's what I take from it when Batman says, "I can do those things...unlike Dent."
The symbol was broken at the end of 'knight', figuratively and literally. TDKR was the gradual rebuilding of his symbolic status staring with rebirth, absence, Return and Blake, right?