Batman doesn't kill, but he will purposely crash a train and leave someone inside, throw someone off a building and shoot at a truck until it veers off the road. In the eyes of a damaged orphan, that's not killing apparently.
That's one of the biggest question marks over Nolan's films, with Bats obliquely breaking his one rule with very shaky justification. Now, it is fleetingly addressed during Joker's interrogation in The Dark Knight, but across the series it's generally just hoped you won't notice the contradictions.
Originally, however, that was going to be a major plot device. Not saving Ra's al Ghul at the end of Batman Begins was to provide a moral dilemma for the character and be a key part of Joker's case against the hero.
You see, following the origin story, David S. Goyer had a two-movie arc involving the Joker and Two-Face mapped out. This fell by the wayside at some point during pre-production, with only very broad ideas (the characters, some of the momentum) crossing over into the finished film. What became The Dark Knight would have ended with a conflicted Batman going against his instincts and letting Joker live, sending him off to Arkham. That's similar to the finished film in terms of where it leaves the characters, but it goes a very different route to get there - sparing the clown was going to be a big deal.
The finished film isn't really lacking in Joker tearing up Batman mentally - the only difference is that in the early draft he was targeting the Batman visage, rather than the more human side underneath.