Except that was not, by any definition, "his original death." The Joker had been around as a character for nearly half a century when that movie came out, and had been seemingly killed a number of times before it. Indeed, he was supposed to die at the end of Batman #1 in 1940, but the editor insisted they add a line revealing that he would survive his injuries.
Sure. It wasn't even Joker's first appearance in a movie either. However, if there was a reference, it wasn't designed to target the audience of pedantic people, but the general movie-going audience who saw Batman in 1989 and The Dark Knight a few years ago and probably didn't read Batman #1 in 1940.