I'm afraid the vids don't convince me. I actually see exactly my point, although it seems to pivot around a lower point, at the moment that the rotor is tilted the lifting force also provides horizontal motion, so it seems to move around a lower point. Again, as much as it is applicable to my perception it is to yours. Your quote: 'Human perception and intuition, on the other hand, are faulty,' And what you see in a video is the same as I do, but with different interpretation. At this moment wel could both be right or wrong.
Just as a reminder, a helicopter is actually suspended instead of lifted. All forces that induce motion originate at the point of suspension. So I say it's still not just CoG / CoM. Look at this little picture.