The issue is lack of clarity, including on the part of many instructors, regarding the relationship between CBM and rotation.
The first thing to keep in mind is that the definition of CBM is not in terms of rotation; in fact the definition doesn't refer to rotation at all. CBM is when the side of the body opposite the working foot moves faster than the side of the body on the side of the working foot. While this has implications with respect to rotations of body parts, it's better to ignore those when trying to execute the movement.
In the case of the Mirko video, which is wonderful, his wind up in the prep step causes him to enter step 1 of the natural turn with a right side lead. By the time he arrives on the right foot, his body has squared up, and as you note, by the time he's stepping off the right foot, the left side of his body is ahead of the right side of his body. This is CBM: the left side of his body, which is the opposite side from the working foot on step 1, which is the right foot, has moved from behind the right side of the body to ahead of the right side of the body, so it has obviously moved farther, and thus faster.
In Standard, turn is normally measured in the turn of the feet. Thus, "no turn on 1" means the right foot lands pointing directly forward - neither toe out nor toe in.
Now, if you are measuring the turn of the hips, independently of everything else, CBM necessarily involves hip turn. From a physics perspective, conservation of linear momentum implies conservation of angular momentum and vice versa; in CBM, that means when one side moves faster, and that hip moves faster, then there's a rotation of the pelvis toward the other side. However, there is no rotation of the feet, and thus no "turn".