I have never heard that military legend before. I don’t recall being allowed to place my hands in my pocket as an Instructor. I would have gotten hammered for being unprofessional.
Maybe he was just joking with a straight face. The correct answer can be found in AR 670-1 specifically:
EXTRACT OF AR 670-1, paragraph 1–9. Uniform appearance and fit
a(3)… while in uniform, personnel will not place their hands in their pockets, except momentarily to place or retrieve objects…
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