The Dark Knight definitely tells a complete story. In fact, I think that thematically, the first two films work better without the third. BB and TDK between them tell the story of the redemption of Gotham City. Bruce becomes Batman to provide a symbol of hope and justice for a fallen city, and in so doing, he inspires the people to begin taking Gotham back from the corruption and lawlessness. But he recognizes that a masked vigilante is a dysfunctional sort of savior for a dysfunctional city. In order for Gotham to become a fully healthy, lawful community again, it needs to restore a working justice system and social structure. Batman can't provide that, but District Attorney Harvey Dent can, at least as a symbol to take Batman's place. So TDK is about Gotham maturing to the point that it doesn't need Batman to save it anymore. Batman's ostracism is the conclusion of that arc, the acknowledgment that Gotham has outgrown his methods and he'd be a liability if he remained.
So TDKR is kind of a thematic reversal. It doesn't build on what TDK established so much as reset things to where they were in BB -- the system torn down by the League, the city plunged into anarchy so that Batman would be needed again. Which is kind of a cheat. I guess the idea was that the lie Batman and Gordon told wasn't a truly legitimate foundation for that reformed civilization and the truth would come out eventually, but the way the truth came out was just kind of tacked on to a story about something else altogether, and it was kind of lost in the shuffle.