1) The chair and the "victim" started out with the same acceleration. They should have ended up in roughly the same place. But...
2) The victim must have weighed much more than the plastic chair, yet he went twice as far. That's impossible.
3) There's the F=ma and [link|http://en.wikipedia.org/wiki/Hooke%27s_Law|Hooke's Law] issues that Drew raised. The force to throw a person that distance is much larger than that produced by a few guys stretching a rubber band a few feet.
I suspect the "victim" was digitally added later (after the "camera giggling" part of the tape).
[edit:] Compare that tape with [link|http://video.google.com/videoplay?docid=-2262706074586564619&q=human+slingshot&hl=en|this one] to see the way a human slingshot should really work.
Cheers,
Scott.