I think others are forgetting that in order for TDK's ending to make sense in the context of where TDKR starts that the Dent lie would have had to have a positive effect on Gotham City.
If you recall, Dent was responsible for a huge Rico. It's only natural that after his death an even crazier act would follow by the authorities and politicians that were inspired by him. So the Dent Act was created.
Logically, the Dent Act made a killing. It would have to be if Batman and Gordon's plan for making Dent The White Knight at the end of TDK wasn't pointless.
And because Batman took the fall for the murders, that made him the last and only villain at the end of TDK's events and all through his retirement. That meant, before Bane showed up, Batman became the last known fugitive.
So the Dent Act works. Batman becomes unnecessary. Bruce sees this as his out, not because of Rachel, but because all the events that transpired led him to this decision with Gordon. Joker could not win, even if that meant he had to go away as Batman and let Dent take over.
And I assure you, if the beginning did not hit it home, Bruce still wanted to be Batman for years, it's just he was devoted to keeping the lie intact because he thought it better served Gotham more than Batman ever did ("Blood on my hands").
TDK's theme of escalation ends with the movie because Batman realizes that even though Dent did kill those people, Joker was right about one thing... it would not have happened if it weren't for him. Batman disappears, the escalation stops. With the mob taken care of, Batman is no longer needed.
So TDKR opens with the lie still in effect. And Bane is the answer to unsurp the lie, which is why he is put in place as reading the note instead of Gordon. Many had problems with this, but this was all about punishment. To have had Batman or Gordon tell the world that 8 years was all based on a lie, that Dent ended up becoming the bad guys he was fighting, wouldn't be quite the shame necessary to get them out of their heads and rise to be heros.
None of this contradicts Batman Begins or The Dark Knight.
So the fans expected Batman to be hunted between TDK and TDKR but not realizing that if Batman ain't there, he's not being chased. Now, I'm sure police were following leads all through those 8 years. It was certainly now much less of a Joke(r) than it was in TDK where "the investigation was ongoing" with pictures of Lincoln and Bigfoot as suspects.
Dent was an honored man, for sure. The movie happens to open with the anniversary hosted by Wayne. People adored this guy 8 years on. So, it's only natural that the people that believed the lie, also believed Batman was a murderer. That would probably be the entire police force. And as soon as Batman reemerges, guess what happens? They forget about Bane and start hunting the Batman because they view nobody else as a villain. With the Dent act, they've taken out so much crime and built up so much confidence, that they consider Bane as nothing, which puts them in the hot seat later. Batman also undersells Bane, which is why he's beaten within an inch of his life.
None of this contradicts Batman Begins or The Dark Knight.