Joker says himself, "Sometimes I remember it one way, sometimes another." Even the dead wife and Red Hood backstory is technically supposed to be looked at as being a lie as well, it's just the backstory he was thinking about at the time.

That said, it's generally accepted as the true story to Joker by fans and official uses. (Along with Barbra being paralyzed.) Despite, from what I understand, the Killing Joke was never meant to be part of the canon when it was made.

Batman just starts following Rocket's style and just yells at all his villians to get their shit together, their so shocked that batman, mister grim and quiet is suddenly yelling at them and self reflect…