Wow, that does all sound very confusing. Let me see if I can help clear it up.
I'll start by correcting what appears to be a very simple typographical error: You referred a couple of times to amount of turn being "1/2 + 1/8", when I believe what you really meant was 1/4 + 1/8, which is quite a bit different. 1/4 + 1/8, of course, equals 3/8, so assuming I'm right about the typo, that clears a lot of it up right there.
The first three steps of a Natural Turn in the Waltz. Quote. " Amount of turn. Make three eighths of a turn on each three steps ". End of Quote. How can that be. Tell me if I am wrong. Thats nine eighths of a turn
3/8 of a turn twice is 6/8, otherwise known as 3/4, and that is correct. To get 9/8 of a turn you would have to have a Natural Turn consisting of 9 steps, which of course it doesn't. If you include the subsequent Forward Change, you get an amalgamation of 9 steps, but Mr. Moore is clearly referring only to the Natural Turn of 6 steps, not the entire 9-step amalgamation. Forward Changes, as we all know, have no turn (At least, not in the feet, but that's a discussion for another day).
The next point is that you seem to be confusing competitive technique, where rules are often bent for the sake of performance, with book technique, which serves as a very general guide to execute figures in a way that is simple, clean, and "correct". You can't fault someone who follows the book to the letter -- everything he does would be considered correct. It's just not going to win any competitions these days. So when you look at a video of a world champion dancing a figure, and try to reconcile it with what the book says is correct, don't be surprised if you find quite a few discrepancies.
One of the major aspects of dance technique that is simply not addressed in the book (and understandably so, as it severely complicates things) is the notion that we very rarely truly move straight forward or back; Steps described as such are actually taken (or commenced, if CBM is involved) somewhat diagonally with respect to the body alignment. This is where, when watching a pro, you might be tricked into thinking they're using a different alignment. In extreme cases, they might actually be (more on that in a minute). But if careful attention is paid to the feet, one can dance a Natural Turn with exacting foot alignments, and still make it appear as though he is quite under/over rotated, especially if you as an observer are watching the whole body and not paying close attention to the feet.
That's not to say that you necessarily misinterpreted what you were seeing. The whole idea of "using diagonals" is sometimes taken to such an extreme that dancers indeed move along a diagonal not just in relation to the body position, but also with respect to the feet. In other words, that under-rotation of the upper body toward the end of 3 that you normally see -- the action that should leave the man pointing against LOD with his feet but with body turned to almost back diagonal center -- might carry all the way down to the feet, so that the man is indeed backing diagonal center top to bottom.
As to whether you yourself should attempt this degree of rule bending, well, it's your own personal decision. I certainly can't recommend it. A dancer of the calibre of the one you mentioned has a tremendous amount of skill, and can commit any manner of sins without paying a heavy toll. (At that level, rules are normally bent or broken as a "trade-off", typically a sacrifice of something small in the interest of making greater gains somewhere else). The average student will likely suffer much greater losses by breaking the rule, which is of course why the rules exist in the first place.
At any rate, you can decide those things for yourself. My goal here is not to advise you on your dancing. I'm simply hoping to clarify what you're seeing when you watch top pros, and how to reconcile that with what you might read in a