Perhaps you should re-read. On thumb-over and thumb-under (TO, TU):

"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."