Well, generally the admonitions are about how the body is relaxed but there are no "wrinkles" along the surfaces, so that it is hung as one unit; the hips and lower back are relaxed while the legs hold all the weight. If the hips are relaxed and the shoulders are relaxed but the overall 'connection' of the body is stretched (not tensed though) so that there are no 'wrinkles', the twisting one part of the body will spread lines of force easily to other parts of the body.
[nikyo example snipped]
So the short answer as it refers to the hip is that the hip is relaxed and not under tension because the weight is sunk into the legs, not into the hips and lower-back, thus leaving the body relaxed and pliably connected.
Just catching up in this thread and wanted to highlight something that was staring me in the face for a long time and I didn't see it, because I thought
I knew it.
Try moving (or just standing) while keeping the above requirements in place. I've found it quite difficult, eye-opening and exciting. CAUTION: your legs just might hate you for it!