Nah it's always been explained on every documentary there's been made about him the same way all the time. I don't really think it's a mystery. And remember pretty much the only skin people ever saw was his face and his arms. His extravagant outfits always covering most of his skin.
He did have the disease you mentioned, Vitiligo, and also lupus, though luckily for him it was in remission, otherwise he probably would have died in the late 80's.
So anyway when this began they simply covered up with white patches with makeup that was the same colour as his skin. Easy. But as the disease progressed, so much of his skin was covered in white patches that rather than cover it up with "black make up", it became easier to cover up the good skin with "white make up", thus, the man appeared to change skin colour.
I'm no doctor so I've no idea if vitiligo alone can really become that bad, but the story to me at least sounds plausible. He admitted he never had his skin bleached... yeah he could lie but why would you?
@Spaz: I think I've seen a video clip of what you're referring to. I assumed it was because he was raped/molested as a child. It's the most logical to me - explains his generosity toward children (wanting them to have a great childhood rather than a shitty one like his?)