I can see that, and no, I don't think it is the camera angle. As to the frustration you are feeling, why not learn it both ways and then decide? One thing I wonder, is would there be less pressure on the knee joint, if the foot pivots rather than staying more fixed? I know knees are capable of a lot of rotation, particularly when flexed, but crikey that looks as if it would make for sore joints!
This video is interesting, showing how "we used to dance pivots using basic technique" and then evolved/advanced technique.
So using basic technique, you step LF back and slightly side and turn on that foot about 1/2 of the turn. It is how it is still described in the books. As he states, there is no rotation or torsion in the body and legs. So whole body turns as one unit, with everything aligned, around that foot and together with the foot. Turn is stated to be on the ball of the foot with the heel just kissing the floor.
It's not bad to practice things this way. It helps the awareness of the upright alignment of the body, balance and actually using the legs to move you. However, if you watch closely, you will see that it's not entirely the case on the demo, for instance at pos 1:50 his LF is still almost backing LOD while his body is already turned at least 1/8 more. And if you look her doing pivoting action, you will see typical usage of the body for the spins - shoulders start turning earlier, then hips catch and overtake the shoulders in amount of the turn, hips stop turning and then shoulders stop turning. And as you see, there is no demo in the couple which would bring more problems
Evolved technique explained after that is taking usage of rotation of all joints in the leg (ankle, knee, hips), just like on the clips with Arunas, Mirko etc. Hip joint is actually the one with most rotational range of motion, but if the knee is bent (as mentioned in the video), its rotational range of motion (relatively small when the leg is straight) also increases. Also, from the demo you can see some usage of rotation in the body as well - shoulders turn slightly in relation to hips before every transfer of the weight to the foot and unwind after that. Whole mechanics is quite complicated. Anyway, for the dancer to take advantage of this, heel has to be firmly on the floor during part of the turn, so the foot turns upon placing the foot on the floor, stops when the heel is lowered while the body continues turning, and then the foot continues turning when the heel is lifted. So it's more like french kissing of the floor ...
One comment simply on semantics though is this: I may be wrong, but I don't think the ankle joint actually rotates. I think rather the tibia and fibula twist around each other within the calf, providing rotation within the calf as bizarre as it sounds. Notice when you rotate the foot, the lower part of the calf (just above ankle joint) stays aligned with the foot. Correct me if I'm wrong.
Here are two more videos if they are of help. I actually sent it to my (lady) teacher a few years ago when we came to disagreement about pivot technique in natural spin. To make it more visible, I reduced the frame rate
One is from Hilton's teaching video. He demoed it solo quite basic way, although stepping more to the side than in the book. But we can see turning on that foot and even some CBMP on the beginning as it was stated in older books. However, in couple, it changed into "evolved" way without any explanation. Obviously, one can't do it exactly the same in the couple because common center of gravity is placed differently, partner has own movement etc, but this difference is much bigger. So even big names are not always aware how they actually do it (this is one of many examples) and this actually evolved long ago. It was danced this way even in 90s and probably earlier
Other one is my recording from a competition about 10 years ago, maybe some things are more visible due to different camera angle. It wasn't really the winning couple and someone might do it better, but they are 100x better than me so I don't care ...
However, she wasn't convinced with this and was very unsatisfied with the dancing of this couple ... luckily next season we got opportunity to return to previous (and still current) teacher where I don't have this kind of problems ...
I just has another Eureka moment concerning pivots: It occurs to me that another important element is with the right foot. The foot appears to pivot about 135 degrees, but the pivoting is happening much faster than the rotation of the body. It's like the idea is to maximized the amount of time that foot is flat to the ground. When I'm doing it now, I feel like I'm consciously focusly on moving that foot as rapidly as possibly. I also notice Mirko distinctly picks up the heel when doing it. See how fast the foot whips around in this clip: http://www.youtubeonrepeat.com/watch/?v=BGx2Lw-9cMc&from=35&to=36. Feels like it adds a lot of control. What do you think, vit?
When doing large steps, I would say the goal is to use the feet as efficiently as possible because they propel you across the floor. Part of that are probably brief moments when the feet are firmly on the ground with lots of pressure to the floor and without any kind of sliding (whether linear or rotation). On the other side, center of gravity moves very smoothly across the floor. So in that sense I would say you are correct, although if I were a dance teacher (which I'm not), I would never say that on the class - it might tend to make a lot of students a kind of statical, while actual goal of dancing is simply to move
So principle seems to be the same in both back and forward pivot. You place the foot on the floor, usually rotated slightly more into the turn than the body (part of that rotation also happens while lowering whether heel or toes). Then the foot stops for a brief moment, while bodies continue turning. It creates torsion in the leg like in a kind of spring. At certain moment before picking up the foot again, pressure of the foot to the floor decreases enough so that it turns back to the neutral position (about parallel with the body), releasing the torsion in the leg, so of course during that it rotates much faster than the body. Here, you can intentionally add more rotation of the feet, placing the foot so that it is at the best position for the next action. So part of that is natural / unintentional reaction of the body/leg and part intentional. My teacher frequently says - just place the foot to the proper position, the rest should happen automatically
Due to various reasons, time when the foot doesn't turn seems to be somewhat longer in back pivot than in forward pivot.
@vit , You'll love this: I had a private lesson with my instructor with a top of the line male instructor. I think he's been top 12 blackpool. He ended up doing the exact same thing Hilton did. He demoed the pivots old style and then when he danced with my instructor he went to new method without realizing it. I called him on it and he said he actually was doing a complete pivot on his left foot. I saw very clearly that he didn't. My instructor was so happy that he proved her right. Ahhh!!! This so so insane!
Most ballroom teachers teach using relatively similar methodology/terminology, based on the book (approved by teachers' organizations) and how they were taught by their teachers. So whole teaching approach changes very slowly along timeline so we run into situations like this. It is just like that. However, despite that, some teachers are quite successful in improving students' dancing (it comes with accumulated teaching experiences), some not at all. For me, only working method is trying the figure with the teacher as both leader and follower and checking what doesn't feel right. Being an engineer, explanations and theory (many times actually pseudotheory) usually ring the wrong bell on me. Human movement is very complex, nobody actually studied all details and even if somebody did, it would be too complex for teaching purposes