The swing begins down. If you think in terms of what the barrel of the bat does (begins well above the strike zone)then the barrel of the bat obviously must come down. The hands ,too, go slightly down at the beginning of the swing. This is irrefutable.
The plane of the swing levels out-maybe slightly up- as the bat approaches the ball. And then the followthrough may be level or up depending on the location of the pitch.
As long as a hitter can distinguish that the swing begins down, but does not continue down to the ground, then "down" is definitely a worthwhile concept.