Lets use your formula, a 25c tire, common to a race bike, at 100psi which is a common race pressure would mean that a bicycle would have to be moving 100mph in order to hydroplane, please show me the pro rider on a pro tour bike that achieves that speed in the dry, they don't because at a certain point its no longer possible for the bike to safely stay upright. It is possible, as your video shows, when the bike has been designed with fairings and more and I doubt you'll find one of those nut balls with the solid brass pair willing to try in the rain. Further, the formula you bring up is a generic one that doesn't take into account things like tire shape and tread pattern, its why tires like goodyear's aquatread and other brands' equivalents can change that equation and perform at higher speeds than a standard tire, by being able to direct the excess water through channels and away from the center section of the tire it increases the speed at any given pressure that a tire will hydroplane. Likewise, the narrow shape of a bicycle tire isn't accounted for in that equation because of its ability to cut through the water, bicycle tires don't need a specially designed tread to move water away, they're narrow enough to do it naturally. As to what speed the hypothetical nut job would need to be at to hydroplane their 25c tire at 100psi is an unknown because while anything is hypothetically possible, the reality is that it really isn't.
Even using a motorcycle tire as a comparison doesn't work, motorcycle tires are inches wider than a fat bike tire, and as a result the fat bike would need to hit higher speeds at equivalent pressure to hydroplane. Dropping the pressure to 36psi in a 25c tire to get it down to a reasonable 60mph also isn't a solution, while it would mean the tire can do it at 60mph using the formula and not the real world scenario of actual tire shape, getting a bike and rider up to 60mph on a tire that will pinch flat at 10mph just isn't going to work. So yes, you've proved everyone wrong, hypothetically you could, in some ridiculous long shot manage to hydroplane a bike. In the real world, its just a stupid argument to even try to stand behind. But have fun with it.