I am not so rue blue looks back to me in the last picture. When your outside leg is long, you are already in your turn. Your missing a critical moment between pics 4 and 6 when blue initiated his turn. By the time his ski is at the gate, his upper body will be ahead of them cross blocking the gate as he initiates the next turn as the skis cut across his COM, which will keep moving in a straight line toward the gate. I see no issue of back seat skiing there.
Now if you look at red in the bottom pic, because he is in the back seat in pic #3, his skis didn't carve property. Look under his skis in pick #5, there is a nice pile of snow all pushed up under his boot and tail of his skis, but nothing under the front half of his ski. That's not a carved turn, it's not a skivit, it's back seat skiing on the tails. OK for scrubbing speed on the bumps. Not so much for getting to the gate fast.
UPDATE - I watched your clip, and, on your original point, yes, there is one point at 1:11 where she is in the backseat during transition, but before you even get to 1:12, she's already come forward and pressured the boot to initiate the next turn. So yes, being "back" in transition is not a deal breaker, as long as you can recover in time to make a clean turn at the next gate. On your point about "seeing the outside foot going back while getting straight", I think you are off in your analysis. The leg comes straight as the ski is in the apex of the turn and you are riding it around at that point, not, I think, at the initiation, which is when forward pressure is critical to carving cleanly. At the start of 1:12, you see a textbook initiation, where the left leg is flexed, the knee is driving into the ski, and her shoulders are in front of the outside ski. Hard to see what happens in the next turn, but at 1:15, the turn is back and you can hear the sound of speed being scrubbed just a little. What might have been going on is adjusting her line to head into the next double gate (remember, she is lining up for the next gate at this point). So much is going on in a slalom run like this you can take a single turn and say, "Gotcha!, there was a pro skiing not applying forward pressure on one turn so why should I worry about staying foward.... " In a slalom, your COM is trying to travel a straight line in line as much as possible with the fall line. You skis are twisting in and out of that line. You want your skis to come around from being behind your COM at the start of a turn, to even or slightly behind at the apex / finish, and as they run back across your line of decent, the body, which continues in a straighter line down the hill, passes the skis, and you end up in position again (COM in front of ski) to start the next turn.
Edited by gdeangel - 2/18/14 at 7:27pm