I have both a boar and a badger, and I use the boar more often I have to confess, I think the main reason is that the badger one is a lot fatter and tends to get suds from a to b.
I was considering getting a synthetic too for no other reason than that I suspect they dry a lot quicker which might make it useful as a travel brush, but the reviews I've heard about their abrasive coarseness put me off a bit.
That video was obviously a blatantly biased piece of advertising and I doubt anyone in their right mind would trade in a badger for a synthetic, my guess is since the preference for badger over both boar and synthetic is alost universally recognised they've had to stoop to some misleading tactics to boost sales.
Manufacturers, being liberal with the truth to sell shaving products? perish the though, surely THAT would never happen. :)