The adherence to a continuity is for the sake of staying somewhat faithful to the source material. If you're going to change things without it serving a function, why adapt it at all? Why not just create something new? As an example:
You people are missing the worst part of this news.
Veidt is "a costumed adventurer who retired voluntarily, disclosed his identity and built a large fortune. He hatches a plot to avert a global catastrophe he believes will be caused by Dr. Manhattan."
What?
By your standard, who cares about sticking to the strict continuity? I myself outright did not care for the graphic novel to begin with. I do, however, understand that there are many devout fans of it and can't see the reason behind unnecessarily changing things from the original source material.
In terms of your analysis of his origin, you're neglecting the timeframe of the confusion. It's canon that he was knocked into the chemical vat while being pursued by Batman. This is canon because Batman was there for it and remembers the occurance. It's been in every single in-continuity version of the Joker's origin. Before that, only Joker himself is witness to what really happened and is subject to confusion, but from the chemical plant incident on, it's all documented.
My entire point is: why change it? Making it makeup isn't going to make it any more accessible to the moviegoing audience, so why raise up a big ol' fuck you to the continuity sticklers if it's not going to improve the film material for anyone? If there's no gain to be found in the adaptation, just leave it as it was. A good example would be the concept behind Phoenix in the X-Men movies. Whether you enjoyed the execution or not, the concept was solid. Doing the whole cosmic thing would've been completely impractical, making it a split personality for the sake of the confined time limit of the movies made perfect sense.
Conversely, why change the Joker? We know he's scarred, it shows in the set pictures and prerelease material. It's no less practical to have him come out of whatever scars him white as a sheet than it is for him to actually apply the makeup. In fact, doing makeup would require even further explanation AND would go on to confuse people who saw the Burton movie, watched the cartoons or read the comics, thus annoying a good chunk of the probable audience. All told, Joker's origin in the Burton movie took all of maybe five minutes of screen time, there's no reason to change too many of the standard details.
I think this is all going to wind up as a moot point, though. I think people are blowing it out of proportion. It looks to me more that the scarring and whiteness are blotchy as opposed to him actually applying makeup. Not to mention, most rumors and interviews allege that he's basic the Joker primarily off of the Killing Joke.
In terms of Dent, I've heard more rumors leading that the Joker does it during trial. Beyond that, the timing is less important to the character than the actual scarring and split personalities.