The hands don't necessarily be directly below the shoulders for the shoulders to move on a vertical plane. The only necessity for the shoulders to move vertical is to have the upper spine horizontal to the ground. The arms then could hang below, inside, or outside and the putter would straight back and through.
The feeling of coiling or turning the shoulders does not carry into putting because the plane angle is more vertical than with a longer club. So the shoulders are moving back up and in, but on a steeper plane and the feeling becomes more of rocking. But don't putt by rocking the shoudlers, just practice moving the shoulders in plane at home.
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