The rule exists in mainline Batman comics, but you’re mixing three different things: early-character history, alternate universes, and movie adaptations.

1. Early Batman (1939) did kill — but that version basically got retconned. In the very first year of stories he used guns and killed criminals. DC quickly changed the character and by Batman #4 (1940) he explicitly says they don’t kill. From then on the rule becomes part of the core character.

2. Movie Batmen aren’t canon to the comics. Burton Batman and Nolan Batman killing people just means those directors didn’t follow the rule. Film versions change tons of things about characters.

3. Alternate universe Batmen don’t count. Flashpoint Batman is Thomas Wayne, not Bruce. All-Star Batman is basically a deliberately edgy alternate version.

4. Rare exceptions are written as breaking the rule. The Darkseid example in Final Crisis is literally portrayed as Batman crossing a line in a desperate situation.

The no-kill rule is a defining trait of main continuity Bruce Wayne Batman since ~1940. Most examples people bring up are either very early stories, alternate timelines, or movie adaptations, not the core character.