The theory of preventing death rolls is to eliminate forces that might cause the boat to roll:
The reason you keep the vang (kicker) tight, is to stop the sail twisting. Twist means that some of the sail forms an inclined plane, which generates a vertical component of force and THAT will cause the boat to roll. Theoretically a flat sail will not cause the boat to roll.
Going onto a broad reach means you have to hike out to balance the sail's force. I find that in strong winds it's easier bear off from a reach onto a run and move in to sit on the deck of the boat. I'm talking about gusts over 25knots. Having the sail at any angle other than 90 degrees means you are generating a side force across the boat; which causes the boat to roll. Theoretically a flat sail at 90 degrees will not cause the boat to roll.
Sailing by the lee means you have a curved sail, and have angled the sail and are sailing at a bearing to induce a flow along the leeward side of the sail. This is faster than running square, because a larger force is generated by bending the wind than by catching it. When the wind is gusty, this force suddenly changes, which causes the boat to roll. When the wind is shifty, either the flow suddenly becomes turbulent or you suddenly gybe. So either the boat will roll or you will have to duck and try not capsize in the gybe. Theoretically, sailing by the lee is very hazardous during strong winds.
In the video above, one comment heard is "the sailors are constantly moving their body weight from side to side, and trimming their sails in and out." I draw your attention to Rule 42.2 Prohibited Actions: "these actions are prohibited: a) pumping: repeated fanning of any sail by pulling in and releasing the sailing... b) rocking: repeated rolling of the boat, induced by (10 body movement, (2) repeated adjustment of the sails"
To put it bluntly, I think the advice given is illogical and illegal.