See edit to my previous comment. With that in mind, let me provide a counterexample to disprove the theory in the video.

Counterexample to theory in the video: See comment by u/Jellytree above.

Galileo gravity experiment. Galileo dropped two objects shaped the same [eg: hollow steel ball and solid steel ball] but weighing different amounts. Both objects landed on the ground that the same time. This experiment has been repeated countless times (including by me) and it never fails. If it's all buoyancy, why don't they fall at different rates due to their different densities?

Meanwhile, the combination of theory of gravity and thermodynamics offers an easy explanation for buoyancy:

When water replaces a less dense object, the net potential energy (determined by distance from center of the Earth and mass of object) of the system (object + water) is lower. And due to the laws of thermodynamics, a system tends to find and stay in a state of lowest potential energy (i.e. the most stable equilibrium).

Buoyancy would fail if you take a less dense object below the water level and then freeze the water because the molecules of water are not moving far enough, and the system cannot find its most stable equilibrium until they begin moving far enough (i.e. after the ice melts).

EDIT note: u/Afks I made some edits to both comments to add clarity in case you read the previous version.