"There is at least one of us who thinks that a left side leading into a Reverse movement is correct and also without any CBM. I would ask how do they propose to do either a Fallaway or a Double Reverse Spin with the left shoulder and side leading and without using CBM where it is required."
Actually, I personally believe that reverse turns do have CBM, but it is a unique kind of CBM applicable to reverse turns, and in no way even remotely a mirror image of the CBM applicable to natural turns. To put it briefly, the shoulders are about the last thing to turn, with everything else (especially the hips) turning substantially before.
There is another viewpoint which seems to have more support amongst world class teachers than mine, and as a result it's something I have to consider. And that viewpoint is that REVERSE TURNS DO NOT HAVE CBM. Those are not my words, but the words of assorted individuals engaged in training current world finalists and champions. These teachers insist, and use specifically the foxtrot reverse or the double reverse spin to demonstrate, that there is no rotation until very late in the first step, possible even the second step. And as we know, rotation to the left on the second step cannot technically be called CBM. There is rotation to the left in a left turn of course - but if it is too late to call it CBM, then there is no CBM in a reverse turn.
The view you really will not find supported at a high level is that the top should turn left into step one of a reverse turn. It just ain't done that way by leading dancers.