As kind of tortured as Batman's "no killing" rule is in the Nolan trilogy, what you describe here is equally tortured on the other end - and one of the things about the no killing rule in the comics that's always strained credibility.
Batman doesn't save Joker in that story because of his extreme dedication to the preservation of all life - he saves Joker because no writer can kill off Batman's main nemesis for good. That's 85% of why the no killing rule was invented - that way all your villains stay around forever so you can have endless rematches.
So while Bruce's sloppy application of his no killing rule in the movies makes him come off as creating a neat little rationalization to feel like he has a clear conscience, his obsessive application of it in the comics does the same - except now it's, "I know you're a vicious murderer who has figured out how to beat the system over and over again, but I'm just going to put you back into the system knowing you'll kill again, but I won't take responsibility for taking you out so my moral conscience is clear, we good? Bye!"
I have to disagree. Batman saving the Joker is no different from the duty of any police officer, rescue worker, or doctor to save every life placed in their care. It's not any of those people's job to play judge, jury, and executioner. It's their job to save an endangered life. It's one thing to use deadly force against someone who presents an immediate, active threat to another person's life. But if that person is injured or unconscious and poses no immediate danger, then there's no justification for killing them, or for letting them die. Your duty is to rescue the person in danger.
There's a Canadian-made show called
Flashpoint which is based very authentically in the real procedures of a Toronto special tactics/rescue squad, and the issue of "priority of life" comes up sometimes. There have been a couple of episodes where an ally of the team, a fellow law-enforcement officer, tried to take revenge on someone who killed their partner or fiance or whoever, and the team's duties required them to protect the killer even if it meant shooting the cop, because priority of life means that you save the one who's in danger and target the one who's threatening them, period, regardless of their respective motives or morality. Only the immediate situation dictates your choices. If you have to kill a friend and colleague to stop her from shooting a murderer, that's what you do, because your duty is to uphold the law.