Although Pivot Slips should, ideally, involve parallel skis, the difference I'm describing becomes dead obvious when the two skis don't pivot at the same time. If there is a "stem," with the outside ski pivoting "tail out" first (quite obvious in most of the skiers in the Snowstars clip), it is a pushoff. If it shows any sort of divergence ("V") at the initiation of the pivot, where the inside (downhill) ski pivots first, with its tip moving downhill and away from the other tip, it is the "release and guide" activity I'm looking for.
The release of the downhill ski, which might possibly create the "V" as Bob describes, but which ideally will not, does not require any unweighting of that downhill ski. This goes hand-in-hand with the other requirements: no stem, no up move, etc. If your balance and edge control are accurate, the weighted ski will release and you will be able to allow the tip to drop downhill with minimal twisting effort. You'll have to add some twist, but if you find that you really have to muscle the skis around, some refinement might be in order.
Here's another mantra for the pivot slip: Do less.
Find the balance and subtle edge control that let the pivot slip happen with minimal action and muscle on your part. No platform. No stepping to the uphill foot. No up move, no down move. No upper body twist. No shoulder action. Do less.
You can start with a pure pivot slip, and, by modifying the skill blend (and/or DIRT, if you prefer), you can move through short and medium radius turns and on to a pure arc-to-arc carve, all with the same fundamentals. You can execute the key release move and, with the right timing, get the terrain to help you "schmear" through the bumps. You can release with the skis underneath three feet of powder and achieve a low-effort arc and a face shot at the same time. No need to bring them to the surface and strongly steer them. (But you can if you want to - that's fun, too!)
The "equal and opposite" force comes from the other foot, but I contend that accurate balance and edge control allow gravity to contribute some (or even most) of the force required to get the movement going. We are trying to let the tips go downhill, after all! Gravity helps.