Refusing to cure a wound with maximum efficiency, or neglecting to kill an opponent with maximum efficiency, as a result of deep emotional entanglements does not constitute asking for or deserving death. People typically live regardless of the inevitable mistakes they make, and in most cases where those mistakes result in something terrible, the existence of fault on the part of the "victim" does not cancel out the terribleness.
The Hound could live, and the wound might turn out to be an insignificant footnote. It could also become infected and result in his death, but that happening would not mean the Hound retroactively actually asked for death when he refused to be burned. You could seriously use this "well, he was asking for it!" logic to diminish the tragedy of virtually every significant death on the show, but I'd say that's an overly simplistic way of looking at things.
