My weight is not shifting on the jerks, I can tell you that. On Saturday I C&J'ed 135kg, my jerk does not move forward or backward at all. It goes straight up, I know this because my recovery is quite easy.
Regardless, I really do think we are talking about the same thing and that we espouse the same technique; we are just explaining it differently. What I am saying is this: NO, you do not have any horizontal component, you should be going straight down. We agree on this. BUT, if you let your butt follow your heels with no hip drive, YOUR BUTT WILL GO FORWARD. Therefore, to make the butt go STRAIGHT DOWN, you have to SIT BACK in your hips while your KNEES ARE GOING FORWARD. This causes you to go STRAIGHT DOWN. I repeat, there is no horizontal component.
Like I said, I really do think we are on the same page. I see the girl in the video sitting back in her hips in order to go straight down; you don't. That's OK.
Best of luck in your training, and this is my last word, lol.