Is this a quiz? Or is it a request for opinions? Anyway, here’s my take.
"Canoes are designed to weathercock”. That statement is a load of crap. As evidence, I point to my guide-boat (a very canoe-like boat - not many people, even paddlers, are able to see the difference between a guide-boat and a canoe). This boat is perfectly symmetrical in every dimension. Yes, it weathercocks, but the fact that a perfectly symmetrical boat weathercocks should be enough to convince anyone that something other than some “intentional” design feature is the reason. Another clue is the fact that weather cocking gets more and more pronounced with increasing speed, but when the speed is zero, the boat is in equilibrium only when directly broadside to the wind. In fact, the cause for this kind of weathercocking is something that has been discussed here before, and that is the way that the stern of a boat “gets looser” with increasing speed. Taken to extremes, when I’m surfing a wave at 11 to 13 mph in that boat, the stern gets so loose that it takes extreme attention to detail to prevent the stern from skidding off to one side so abruptly that I’d wipeout if unchecked, and with a direct tailwind one can’t blame that on the wind. Also, any canoe paddler who has gotten a tow from a motorboat knows that as speed increases, the stern of the boat gets really squirrely and will skid out to one side or the other in the same manner if the paddler is not extremely vigilant.
Bottom line: Absent any other unusual design features, canoes weathercock because the stern skids sideways more easily than the bow when the boat is traveling forward, so as the wind pushes the boat sideways, the stern moves fastest/farthest causing the heading to veer into the wind.
“If wind is coming from the offside, more aggressive J strokes will be required to go straight” and "If wind is from the onside, the correction part of the J stroke can be skipped or if strong enough sweeps may be used”. This seems to make sense but it isn’t a hard and fast rule. Even if I can’t at the moment recall which side for paddling creates more need for correction and which reduces that need, I do remember that a solo canoe that I sold a few years back (a Wenonah Vagabond) behaved in the opposite manner as the canoes I have now, at least for most angles of crosswind (but it would behave the same way for a small range of angles of crosswind. Go figure. My other canoes act the same regardless of the angle of the crosswind, and are thus much less fussy in their handling than was the case for that Vagabond).
To my way of thinking, all one needs to know is that when paddling in a crosswind, if the boat’s tendency to veer toward the offside is too strong to be comfortable, paddling on the other side instead will solve the problem. This is a good reason to practice enough on both sides to avoid having “a good side” and “a bad side” for paddling. This is in agreement with the video, but takes into account the fact that not all solo canoes act as expected.