Okay, here's a theory that just came to mind:
Justin Bieber is signed to Island Def Jam, which is run by L.A. Reid, who recorded Slave to the Rhythm with Michael in 1989. Like many of the producers who worked with him, it is a good chance that Reid still has a copy of the multi track for the original recording. Let's say Reid says one day, "Hey Justin, I have this song I recorded with Michael years ago. Wanna go for a posthumous duet?" Justin says yes, Reid hands over the clean acapella and Justin records his own version. Fast forward some time later. Justin submits his reproduction to the estate asking for permission, they veto it, and he gets pissed off. So what happens? He and/or members of his team anonymously leaks it himself, knowing that it'll create buzz, and bask in the glory that the world finally got to hear a Justin Bieber/Michael Jackson duet.
This just came to mind. Of course the idea that he leaked it himself can be debated, but considering that Rodney Jerkins says he had no involvement, and the estate say it was unauthorized, it's the only other sensible explanation why Justin would get the clean acapella. Thoughts?