The commentator in questions is Iain Percy, a 2-time Olympic gold medalist, the tactician on Team Artemis, and one of the world's best foiling sailors. Pretty sure he knows that he's talking about.
Iain may know what he's talking about, but his description in the video is nonsense. (Time limit, target audience, and so forth, I presume.) I can visualize how you might be able to sail on current power, but it's not “Drift until you get up to 10kt, turn around, and, presto, you go to the source of the Amazon at 30kt.”
Here's how I picture it. (First let me say I know almost nothing about sailing, and in the very likely event that I'm wrong, well, it won't be the first time.)
Having some aviation background, when I sail my boat I rationalize it as an airplane with one wing sticking up in the air and the other one down in the water. If I'm reaching or above, the wing that's up in the air is converting energy from the wind into motive force and the wing down below is using the water for leverage to make that energy move my boat forward instead of sideways. (I have a visualization that involves stalls and spins, but we don't need to go there for this discussion.)
I can't reverse the roles and make use of the energy in the current for propulsion because my sails can't get enough purchase on the air to effectively direct the force that my keel is not very effectively capturing and direct that force the way I want it to go. (I sail on a river all the time, and I'm pretty sure of this.)
Those AC boats are whole different kettle of worms, though, with their super efficient sails and foils. Turn your boat (or the world) upside down in your mind and imagine your keel slicing through still air and your sails filled with flowing water, and maybe you can see what I'm thinking.