Because fluid dynamics is exactly the same as a conveyor belt, right? I'd expect someone that professes to paddle whitewater would know about ferrying...
Under the assumption that the current is the same throughout the water column, no, there's no difference at all between that and a conveyor belt. In reality though, the current is not generally the same in the center as it is closer to shore.
Nonetheless, if I'm sitting in my kayak in a very fast, even current, it makes no difference which way my kayak is pointed - relative to nearby objects floating in the river, I continue moving with the same relative speed, regardless of orientation. In fact, in some water I've been on, it's quite eerie - you'll be playing near a large log that's floating, and it's almost like being in the middle of a calm lake - your movement relative to the log is unaffected by the current - exactly like my treadmill example. But then, you look up at the shoreline, and it's whizzing past.
As far as swimming toward upstream in whitewater - you always head downstream feet first, feet up high. You generally don't want to be perpendicular, because it's really going to suck if you get wrapped around a boulder. Feet up, because if your feet are low & get wedged between a couple rocks or something, you are dead. But generally, you're not worried about how far downstream you end up, lest there be a 600 foot waterfall at the end. Hence riding out a couple hundred yards of whitewater.
And ferrying - generally, it's not ferrying when the current is 3 times faster than you can paddle. If you could ferry across the river while swimming, then being swept over a falls is not a concern.