Like Nick, I've been in a "100-year flood" (which seem to happen pretty darn often, but that one in 1978 did damage trails in the GCNP that took many years to repair, so maybe. . .) . And I've been in lots of slot canyon, some after incredible storm damage.
I'd never want to be in a slot canyon while a monsoon rain was happening anywhere upstream. A co-worker experienced that while gold mining in South America - why is the water a foot deeper? What is rumbling noise? and then scrambling up the ropes as a wall of water came down on them. The guys in this youtube were not in a terribly threatening situation. They got wet. They got muddy. I didn't hear any boulders tumbling down the canyon walls (I found that a particularly scary aspect of being in a canyon in a downpour). I didn't see rocks, logs, etc, getting washed downstream. I didn't see the canyon bottom filling up with 10 or 20 feet of water.
It looks like there are doing what cavers call a "pull-down" trip in which you pull down your ropes as you go. Some of the most harrowing stories in the annual summary of US caving accidents are on such trips. You're committed and if there's an injury, the cave has changed, or the weather changes, you're still committed to do the whole thing. Pull-down trips require more planning, more contingencies, a stronger group, and a more conservative response to weather forecasts. They just do.
My first thought during the video was, "Why are they telling guys to come DOWN and then happy they did?" I had other thoughts about "WTH is his hand ABOVE his figure-8/ATC?" because my hands are only ever BELOW my rappel device.
But back to the chaffy nature of this thread: When we were soaked through, with sticks and rocks in my hair, getting hailed on, we ducked under an overhang and were appreciative of the insulating properties of large German tourists who were towards the outside.