I suspect that with "mastery of a skill" comes an ability to understand "mastery", in that - on a variation of man-with-a-hammer syndrome; holding the mastery of one area will help you better understand the direction to head in when mastering other areas, and learning in other areas.

to me the line now reads; "mastery of [subject] isn't just about [subject matter]: mastery teaches you how to think"

where <subject> can vary; the significance of what people are trying to convey is maybe not in the <subect> but in the experience of learning.