I have swayed many miles with overloaded pickups, towing everything from asphalt rollers to skid steer loaders. Believe me, I know what sway is. When the oscillations start and won't stop until speed is reduced dramatically, that is sway. The tow vehicle is not up to the task. When someone posts three or four absolute "Rules", I question their expertise. I am not nearly arrogant enough to attempt to list all the factors in sway.
To paraphrase your signature. "Too many opinions and not enough facts".