As someone who has ridden 28s for decades, loaded and unloaded, I can certainly attest to riding unloaded on 28s over rougher roads allows me to ride faster, more comfortably and with higher and more secure cornering speeds than a lot of roadies on 23s or 25s at high pressures of 110 or 120 or whatever.

I'd already seen their vid, and while it is really talking about road bikes, ie wide is 28 vs 23 or 25, I do see that on a touring bike, wider tires certainly makes things easier on rims and spokes--but it really depends on the road conditions and surfaces.
With loaded bikes, I've ridden with 1.5 and 2in tires, so 38mm and 50mm, and the 38s are certainly a good compromise in my opinion in that they roll pretty nicely on good pavement, but do have the volume at lower pressures to be softer for rough roads.