You appear to have a sever confusion between the conditions at the initation of an action and at the conclusion. The difference that you find surprising are key to a solid initiation, but they do not necessary persist to the conclusion.
"Anonymous. Have you had a look at the Learning Center, with the overhead shots. Please don't tell me that the lady on a heel turn, Double Reverse or not. You would have her turning the hips without the top."
At the start of the action she should be, yes. But you will probably not see that here as they make the mistake of curving the path of movement - something the classic texts explicitly warn against. This completely changes the method of CBM away from the traditional technique to something different.
"Are you turning into step one or at the end of step one."
Both. Hips turn into, top turns at the end of.
"I think if you are not careful you would lose contact your partner."
No, this is precisely what enables a clean hold throught the figure. If you turn your top into step 1 you shove your partner off track. If you neglect to turn your hips into step 1, you have not lead any CBM...
"And this is the acid test, turning with two straight spines or two twisted. Which is it."
Both. Early in the action it is with two twisted bodies (as has been pointed out, it is more other body parts rotating different amounts around the spine than the spine twisting) later in the turn the hips and shoulders may align, then may differentiate again by the end, depending on the type of ending.
But the most obvious example of where a different hip and should alignment is needed is in promenade. There's a clip somewhere on this website showing 90 degree of difference between shoulders and feet. I find that extreme, but they manage it - and a healthy chunk of that difference is between hips and shoudlers. Personally, I prefer to move digonally across my feet, which means that my foot to shoudler difference is much less, and my shoulders are more closely aligned with me hips. But if as many you allow your hips to turn out on the step through (a mistake, most figures actually call for CBM rotation towards the partner there) then you will have a substantial hip-shoulder difference in promenade.
"Lets remember you are still under the opinion that on a Lock Step the hip goes without the top."
Yes, that is the proper and nececessary commencement of a backwards partner outside movement. You can deny it all you want, but it won't change basic facts of the human body and dance hold. - it is that isolated diagonal pull back of the right hip relative to the rest of the body which gives the partner space to come forward. Leave it out if you want... you are the one who will look like an off balance fool...