Was Freddy Krueger always meant to be a killer from the start (pre-lynching?)

Most fans know that the filmmakers planned for Freddy Krueger to have been a child molestor in his backstory, but changed their mind sometime during production. It's usually taken for granted that the idea was that he molested the kids in addition to murdering them, but do we know for sure that was the case?

I ask because it occured to me that the backstory with the parents' mob justice actually works a lot better for the story if Fred Krueger did not turn to murder until after the parents burned him alive and he became a dream demon. Since he wouldn't have been so much of an active threat (most child molestors go after kids they know rather than go around stalkng random victims), the parents' actions come off purely vengeful, and it's easier to see them as being responsible for Freddy becoming even worse.

With Freddy having always been a serial killer, though, the parents actually look pragmatic (hell, maybe even heroic), like they were simply desperate to try to put an end to an active threat, and that it just didn't work in the end.