The guy in the video did it wrong. He tied it to the string. I haven't heard of anyone getting it caught on the string. I am not saying that cant happen, I have just never heard of it happening. The situation occurs (that I have heard of), at the rest with the string getting looped on the rest, thus you have enough slack for the arrow to go a few feet or yards then it will snap back like a rubber band.
There was a teenager that died here in the DFW area last year. The glass arrow snapped back and penetrated his eye going into the skull and it killed him. I will post more links below so you can read up a bit more on it. It does and can happen. Like i said, if people don't believe it and want to continue, cool, good luck. But for those that would like to know if it is dangerous or not, I personally, would want them to know & not try to convince them there is nothing to worry about, not only have some had serious injuries by doing this, some have died. Life is great, why risk it?
In fact, the death by this very scenario (tieing the line to the end of the arrow)
inspired the AMS system itself.
Read about it here ->
http://www.womenhunters.com/ams-article.html
More - The thread paints a good picture, but the pics are no longer available. But you get a pretty good picture of how bad this injury was. Arrow snapped back and hit is hand where holding the bow. He ended up loosing the finger completely. It couldn't be repaired.
http://www.pensacolafishingforum.com/f21/bowfishing-accident-85137/
Google it, I think you might be surprised as to how much this happens. Once you see how many times this happens a year, it gets pretty hard to say "dont worry about it, nothing bad is gonna happen" if you dont use a slide.