Edit: Seen both videos before.. (sorry double post).
Isn't the original much slower? If you speed it up, you'll get a fast vibrato in most songs with vibratos.although I don't believe it there is a possibility that overprocessing CAN cause a vibrato to go all goaty,
listen to this remix of Always by Erasure:
http://www.youtube.com/watch?v=3KbOBSgKUxQ
Original version does not have this "goating"
That said, "All I Need" has substantially less goating yet I find that track to sound the most like Jason, especially if you take in the possibility the tracks were up-pitched. I think although something was done to the singer's voice (ie adjusting equalization or something to make the voice sharper and less "mellow") I still think it's not enough for it to "sound like" Michael.