"There is no sideways component. Please don't try to put words into my mouth."
I quoted you exactly, when you said:
"but more like the lady's next step (back and slightly leftwards)."
So which of your conflicting posts was your mistake? Your denial of a sideways component? or your mention of a leftwards one?
"Relative to the body position, the foot moves directly back (back, not side). That's what I said: that's what I meant."
No, you said, and again I quote exactly, "(back and slightly leftwards)." You might also want to remember that basic principles of execution mean that the previous step is going to be turned notably less in the body than the foot alignment given in the outline - even a step directly down the LOD would in practice be somewhat sideways "relative to the body position" as you put it.
""The key realization is that an NST is primarily an inside of turn action, much more than it is a pivot action."
No, it's rather obviously a pivot & spin."
As anyone with any real experience of dancing is aware in their body if not their mind, it is a swinging change of places followed by a spinning one.
"Almost. To really understand the situation it is necessary to realize ..."
I don't think anyone agrees with you."
You might want to read up on footwork, as you clearly don't understand it's principles. A backwards step from a lowered position departs the standing foot via the heel, regardless if there is or isn't rise.
"At least I can agree that step 5 (as man) isn't taken in CBMP, although the Revised Technique does say otherwise. Howard is more accurate, and this is one of the small differences between ISTD & IDTA technique. He says (correctly, in my view) that the RF is held in CBMP while the man pivots on step 4. That CBMP is lost on the following step because of the nature of the spin that follows."
I rather firmly believe it to be an editor's error in the first place, not a difference of substance. The cbmp is actually lost well before the spin, as skilled dancers know to underturn the quasi-pivot (if they even do one at all) in order to enhance the swing into the spin.
"I don't think there's anything else to say about this figure: we aren't in a beginner's class."
Especially in a beginners class, one should not make the mistake of trying to complete 180 degrees of turn over the foot, but instead should be instructed in basic movement principles, such as the use of swing to connect the footprints with flow and musicality. Having a teacher with the knowledge and experience to explain such things is the primary differentiator between a situation where students will work hard while going nowhere, and where students will quickly graduate from beginner classes to ever more capable dancing.