This always confused me in TDK. When Batman and Joker are on the scaffolding and Batman throws Joker off and then catches him with his gizmo, the Joker teases him for not breaking his rule. In fact, his "rule" was a big part of TDK.
However, if we go back to BB, did he not "kill" Ra's Al Ghul? I mean he said "I'm not going to kill you, but I don't have to save you". Though I would say that he was ultimately responsible for his death. Did he not kill a whole temple full of League of Shadows' soldiers, including the person who he originally thought was Ra's?
Nah, he walks the line between directly murdering someone - and people that die due to other actions he may have a role in. He didn't kill Harvey, although Harvey dying was a result of Batman's actions. He didn't kill Ra, he just didn't help him. He started the fire ... but he didn't actively murder any of the LOS.