That would be a good explanation, but people don't really know much about that 'condition'. It probably wouldn't perfectly turn him white, or even just his face. I have it actually, but just a tiny spot on my neck.... that really isn't noticable at all. I'm just saying, he'd have to have an EXTREME case of it in order for it to be all over body. And it would be really really weird for it to be on his face only. It probably wouldn't be clown white either?
See, I technically have it according to my doctor, but its hardly like OH MY GOD ARE YOU WEARING WHITE MAKEUP ON YOUR NECK??
Either way, I'd rather him have the makeup then vitiligo. Especially since people seem to only pay attention to really extreme cases of vitiligo and having the joker have it would probably just give it an even worse rep. I'm just saying.