Originally Posted by Joker
I always assumed it was a nod to the comics where he has multiple possible origins about how he became the Joker.
"Sometimes I remember it one way, sometimes another. If I'm going to have a past I prefer it to be multiple choice"
In fact that was the Killing Joke thing done right.
In TKJ the Joker says that but it is obvious which story is the real one. The one that's told to us.
In TDK the Joker actually has different origins in his mind. But I don't feel that he actually thinks every one of them is true, but he is aware that he is just misleading people about his identity.