The Joker was not always that, and therefore, there is no wrong way to tell his story. Comics are a constantly evolving story and recreation, so calling it "wrong" when, as noted, there were times were Joker wasn't even written as a antagonist to Batman, but more sympathetically, it shows that he doesn't always have to be "Batman's greatest enemy."
Somehow, this races by the minds of a thankfully small number of viewers. The Joker--like every character--has his origin point, and unlike bad comic adaptations which constantly scream out the "future" and/or a more familiar version of the character (Garfield Spider-Man movies / many MCU films), this film actually takes the time to build the man before the villain, otherwise, he would no better than crap like the Leto version (jump right into insanity) or worse, the Joker from the mid-80s Super Friends cartoon.
Moreover, the Joker's comic identity has never been all about being Batman's enemy alone, or "just" some evil opposite (which was not evident in his first published appearances). He is his own character who happens to know how to bedevil Batman in ways other criminals cannot or will not. But that's a Joker needing years to become the top of Batman's Rogue's Gallery. Nothing happens overnight, and frankly, even if that was a goal for the film, it is not trying to set him up to fit right into the hole of being Standard Issue Joker out of the gates, nor should it adapt the character in that way..