His cape barely slowed down his fall with Rachel in TDK. There is no way he could have saved Ra's. Anyway, this Batman rule is explicit. He didn't say "I'm no killer" like in year one. He said "I'm not an executionner". Which fits this take of the character, which is grounded. He can't always avoid death in his line of work, because he faces extreme situations. Like with the garbage truck in TDK. The guy is oviously dead, but he had to stop it. He didn't execute him, he stopped him, and in the course of events, the guy died. Same for Harvey. He didn't kill him. He savec James Jr, but this lead to Harvey's death.
He won't execute Bane if he can avoid it. but he may have to provoke someone's death to avoid the death of hundreds of persons.