I've seen both videos. Neither one actually tests the tires in real conditions.
Tire width affects the feel and performance for daily driving, snow, sand, mud, rocks, and... Everything. And I'm not just talking about the carcass width - tread width has an even larger impact.
Load rating also plays into this significantly on light trucks like Toyotas since most skinny tires are dually truck tires, and are therefore E-Rated (which are too stiff to perform as designed on a 5000lb midsize truck).
On Toyotas, I've driven tires from 235mm wide with a 7.5" tread width, up to 13.5" wide with a solid 13.5" tread width. "Skinny" tires (235-255mm carcass width) have some marginal benefits in certain conditions but at the expense of road feel, road handling & performance, comfort, mud performance, deep snow performance, and more. I'll never go back to skinny tires.