[MrGando]

It's both the way the technique is described and the name given to it "thumb over" that are unclear and misleading. I know the technique, and in my years of practice (semi-pro) I've never seen it described anything like that. It doesn't even have a "name" per-se, because you learn to play the piano with your whole body, so it becomes a natural thing that you just have to do to get that speed. And by the way, you can still use it when playing slow, if you want to obtain a certain "tone" or "sound".

[packjaddison]

In my head, after 'thumb-under', I think of 'skips' and 'leaps' depending on distance for whole-hand repositioning, which is descriptively accurate for fingering on the piano, guitar, and violin (etc.). Though, for the novice I could see how conceptualizing a movement this way could interfere with legato technique, as it encourages more discrete chunking than does the 'unbroken' thumb-under during a run. Does that nomenclature match your conceptualization at all?