I think "no up" means no reason to elevate beyond TSP. I think Jack is "across" (w/flying rt elbow), not "up". McHatton also suggests that we create a very long "club" at impact...one that begins at the left foot and ends with the clubhead (he holds the club perpendicular to the ground directly above his head). A swing without EA which culminates in one fully loaded, very long primary lever? I think the image of building the long club provides freedom of movement yet incorporates many important alignments.
"The Hat" wants the club swung up, back, and in, via the shoulder turn, and cocking the right elbow/left wrist, with no intentional arm lifting. Dump all the energy downwards and out the arms with the pivot. He is one of the real bargains in golf instruction at $40/hr!