There's some quite mixed up conclusions being drawn here.
Most glaringly mistaken is the idea the the videos here match the English teachers - they don't, as will soon be demonstrated.
In the English tradition, CBMP is not in generally a very twisted position, because the hips stay as parallel as possible. When we speak of the hip at times not being over the shoulder in that tradition, it is not a rotational displacement so much as a linear one - shoulder stretching forward ahead of hip, or hip stretching backward relative to shoulder. On the other hand, in the American tradition CBMP does tend to be twisted - and you need look no further than the promenade video clips here to see that! When you see 90 degree of difference between the shoulders and the feet, it most certainly isn't all below the waist. Instead, that twist is distributed - the hips are turned out a good degree too. Whears in the English tradition they are as parallel as possible, and less foot turnout is used.
On the other hand, rotational actions go the opposite way. There the English tradition does make use of body twist - upper body leading the hips in rotation on natural figures, hips leading the upper body in reverse figures. In contrast, the American method shown here will be much more body moving as an inflexible block, all turning at once.
So what do we have? The answer is that we have a variety of ideas about how things should be done. And quickstep's big mistake is trying to pretend that they are the same, when in fact they are quite different. In each case, one side supports his(?) view, while the other contradicts it. To fail to see the difference between the two sources is to exposte one's inexperience as an observer!