(and I'd like to make it clear that I'm not being negative on these examples, I liked and remembered both these videos I'm just using them to illustrate a pedagogical mindset.)
In this interesting video, the view is put forward that you should cut and step at the same pace to ensure that your hand and body land together. This is so that you cut with maximum strength and for reasons of balance. The idea of not stepping and cutting at the same pace is demonstrated to be wrong.
However, in the below video we have a different opinion, that the arm should slightly precede the body with the foot to follow quickly afterwards to ensure they land at the same time. This is so you can track your opponent if they move. To move with hand and body together at the same pace is demonstrated to be wrong.
Who is correct?
From my opinion they are both right for different situations. Firstly from test cutting I find that you absolutely want the hand and foot at the same pace for maximum effect, moving the hand first and the foot following faster is invariably a weaker strike. Moving the body with the cut seems to allow for maximum engagement of body mechanics and gives you a better draw through the target. However, the second video is also correct if I fear my opponent is keyed up to counter-attack me, i.e. to attack at the same tempo as my strike, then by leading with my arm I can either draw out his response or track his movement before I commit myself. So, both are correct for different situations.
I guess my point is that neither of these people are wrong, but that in terms of how you explain technique it's important to highlight that there are few absolutes in terms of correct/incorrect technique.
When I teach and someone says "is this wrong?" I'm always very careful to say "no, it's just not optimal in these circumstances." The key point being, I think, is that by telling people something is wrong you are closing a door for them. Instead, I feel we should be cultivating a broad understanding of the underlying principles, to analyse and understand. Thus if an opponent varies the timing or measure then suddenly the "wrong" footwork becomes optimal they won't struggle against it thinking "but I was told this was wrong!" and will instead rationalise it and understand what is happening.