For those who don't believe new tires on the rear is a real thing - that the videos were rigged by having bald tires or the driver influenced the result:
The company I used to work for had a demonstration it ran every year. They equipped 3 identical vehicles with a) new tires, b) new tires on the rear, worn tires (4/32nd) on the front, and c) new tires on the front, worn tires on the rear.
We would have dealers drive each of these cars around a skid pad and through a section of the track that was flooded with water (we could control the depth!) Repeat: THEY drove the cars.
Vehicle A drove right through the water like it wasn't even there. Vehicle B lost control at the front, but the vehicle could be steered after it slowed down. But vehicle C ALWAYS spun out - on its own, without any input from the driver.
Complete disclosure: We specified the speed the dealers were supposed to drive around the skid pad - about 45 mph. That was just a bit uncomfortable - a bit higher than what an average person would drive.
The water depth was carefully controlled and we adjusted the depth to get the tires to hydroplane at exactly the right speed.
Some drivers would panic and slam on the brakes. They could make any of the vehicles spin out. Some drivers drove too slowly and none of the vehicles spun out.
But if done correctly, Vehicle C would spin out on its own, where the others didn't.
We ran HUNDREDS of people through that exercise. Lots of folks struggled to reorient their thinking based on what they experienced - it gave some headaches!
I hope this helps clear up that this is a real phenomenon and the recommendation is based on real information.