TDS, I agree with your above statement, but I also see what would be "down across/around the ball" the ball in this clip you also posted....
...especially with his lack of "extension", and a left hand turn around his body, and a back to almost vertical bat in relation to his hands on the "follow-through".
What am I missing, or does that observation make any sense to you also?
I see it more as Betts way of staying inside (hands leading) for pitches up and out within the zone (horizontal plane).. Similar to the feel Trout has accept his is more for an up/in pitch.