I am revisiting this old discussion because I too have realized that I have always played scales using the "thumb under" method.
I am trying to apply the correct method but, even after rewatching the video tutorial and reading the relevant section in Sandor, I cannot grasp the right dynamics.
On page 38 of his fine manual, Sandor writes that "the thumb must be alongside the hand, and able to descend vertically". There is an explanatory image, but it is not applicable to the case in question unless one wants to move the hand obliquely in a clumsy way. When playing a scale, this would involve moving the hand in a zig-zag manner, exactly the way that is discouraged in the video tutorial.
Lowering the wrist helps to decrease the thumb's travel, I imagine.
And yet, in my opinion, the real point to clarify in the technique of the "thumb over" passage is whether the weight transfer must be done in a canonical way or if one can turn a blind eye.
Let me explain better.
If one wants to transfer the weight correctly (at least as far as I know), the finger acting as a pivot (the 3rd or the 4th) must not be lifted before the thumb has fallen onto the next key.
This implies that the thumb will go under anyway. And it is precisely an anatomical issue of the hand. If the "pivot" finger stays in its place before the thumb "falls", the thumb must necessarily go under it. It cannot be alongside the hand as Sandor writes.
I hypothesize that a small rotation of the hand helps. Just a minimum, however, especially in the case of passing under the 4th finger. And I ask the experts if this is a legitimate practice.
The discussion changes, instead, if the logic in the "thumb over" passage is as follows:
Since the thumb passage must be applied to a scale played at speed, such that the movement is extremely rapid and imperceptible, then it is permissible to lift the 3rd or 4th finger an infinitesimal fraction of time before the thumb "falls" onto the next key.
In this case, the movement results as coherent. However, the "canonical" weight transfer is lost (at least I imagine). It is a bit like what happens in the demonstration made by Paolo in the video tutorial regarding Cortot's exercises preliminary to using the "thumb over" technique. At least that is how it seemed to me.