i finally had a chance to watch the video. I'll give a critique, so you might understand what I'm looking at.
He's onto the right idea, tho how he expresses it physically is different than how I would. If you really want power, keep the back heel down and drive that back foot into the ground and use it to drive the body rotation. He lifts the heel and drives back with the ball of the foot. But he's got the right general idea.
However, when he shows the punch at full speed, watch closely: he rotates the body FIRST, and punches SECOND. His punches actually come after the body rotation is completed. That is one telltale sign that he hasn't really got it. That body rotation needs to be happening at the same time the fist is going out. Otherwise, he's just arm-punching. The body rotation has already stopped, so it's no longer giving power to the punch. They need to happen together.
This is a good example of someone who believes he's doing it, but he's not. He's rotating and putting his body behind it, driving from the back leg, so he has reason to believe he's doing it. But his timing and coordination are off, it's not matched with the punch. So in reality he isn't doing it.
That's the kind of thing that I look for, and that's why I say, most everyone believes they are doing this, but most people fail. The devil is in the little details, and the little details make a HUGE difference.