I think you may have answered my question.
Alex Moore's original Ballroom Dancing described (and I'm writing here from memory, not a verbatim quote) that the RF step is danced with CBM, starting to turn to R. [Actually he says RF fwd, turning body to the right]
My rather battered old copy (1986) Revised Technique has that toned down to 'slight' CBM, and no further mention of turn, whereas the current IDTA technique cuts the CBM altogether, and has right side leading (no turn), the standard turn being distributed between steps 1 & 3.
This is an interesting evolution: I was looking for confirmation that the current ISTD technique persists with slight CBM, or does a right side leading now rule the day in both Societies?