No confusion just disagreement with the claim that what you describe is "a properly executed wedge / wedge christie turn" BTS.
Rather than debate what you think is proper and what is not I am going to include a direct quote from two PSIA Alpine Manuals. Considering you work in a PSIA school It might be worth considering their definitions instead of labeling them as somehow improper. I doubt you will agree here but I want to put out there the idea that at most PSIA schools their definitions will be used by the training staff and the line instructors are strongly encouraged to use them as well.
pgs: 66-68-1996 PSIA Alpine manual
The Wedge Christie uses the basic skills of the wedge turn at a slightly higher speed and performance level to link the wedge turn with the parallel turn. It consists of the movement patterns of the wedge turn during its initiation and those of the parallel turn during the arc and completion of the turn. The study and understanding of how the skier "matches the skis into a parallel stance and opens them into a wedge is crucial to the blending of the fundamental skills and improved performance...
..."1. Allow both skis to open from parallel into a narrow wedge with the help of extension and edge release. Begin slightly advancing the "new" inside foot and leg to create a countered relationship between the upper and lower body.
2. At the same time, begin to swing the new inside pole basket forward, along with the wrist, elbow, and arm. The pole swing and it's following touch elp you maintain rhythm and prompt you to move your body into the turn. Note that the movement of the old outside ski off its edge tends to fulfill the stabilizing function of the pole touch.
3. Before matching the skis, you should be in such a balanced stance so that no gross movement adjustments will be necessary to match the skis and remain in proper stance.
4. use the pole touch as a timing trigger. Match the skis by moving your body inside the turn, which will flatten the ski and continue to advance the inside foot and leg. These inside ski movements change the ski's edge engagement in the snow from inside edge to outside edge, placing both skis on corresponding edges- either both left edges or both right edges. This edge change of the inside ski facilitates the increased steering of the foot to a parallel relationship with the outside ski. Because of the increased speed, edge angle, and pressure on the outside ski, the light inside ski is easily matched."...
...Guiding student performance-wedge christie
- Control speed and turn shape by using corresponding edges.
- Move towards the center of the new turn by extending slightly and releasing edges while opening the wedge with both skis to initiate the turn. Actively turn both ski tips towards the new turn.
- Continuously "roll" the knees, and guide the foot from the wedge opening to parallel matching and throughout the arc of the parallel portion of the turn."
pg 46: 2002 PSIA Alpine Technical Manual
Blending movements and skills to create a parallel turn
- After lots of practice and mileage in linking wedge turns, the student will be ready to start matching their skis to parallel.
- Most times, the parallel turn comes spontaneously with a little more speed or more shallow turns on familiar and appropriate terrain.
- Parallel also comes from turning or steering the inside leg (uphill) to match the angle and activity of the outside leg."
So even though variation and interpretations of this exist (especially when it comes to the pole touch) the premise here is the skill blend includes rotary and the skis response to that rotary are clearly identified in both manuals.