To belabour this point for non-pianists, the parent is describing what "thumb over" really is: a sort of physical consequence of playing a fast ascending arpeggio/scale. It isn't an alternative to "thumb under" so much as a good-faith approximation of it at speed. "Practicing" "thumb over", as in this YouTube video [0], would likely threaten the mapping of fingers to keys in a newer player. It's not wrong to acknowledge its existence, but IMO it's properly conceived of as a skill that develops as a consequence of playing normally (though quickly), not an alternative to it.

Because (and in spite of) the fact that he doesn't play piano, his observations on "thumb over" are interesting, but unless you're already aware of the true nature of "thumb over" his authoritative tone will lead you astray in terms of conceptual categorization.

[0] https://www.youtube.com/watch?v=ZLTbURVEEO4

[1] https://fundamentals-of-piano-practice.readthedocs.io/chapte...

"Both methods are required to play the scale but each is needed under different circumstances; TO is needed for fast, difficult passages and TU is useful for slow, legato passages, or when notes need to be held while playing other notes."

"Beginners should be taught TU first because it is needed for slow passages and takes longer to learn. The TO method should be taught as soon as faster scales are needed, within the first two years of lessons."