TDK6--May I suggest that this "argument" is probably not a dispute over the facts, but it merely reflects the difference between being technically accurate on one hand, and giving simple, practical direction and coaching to make the right thing happen on the other.
You are right, of course, that you can tip or flatten your skis by just using angulation movements--feet/ankles, knees, hips, spine, etc. But the critical issue here is not just tipping and releasing the edges. It is the movement of the body (center of mass) downhill, into the turn (in other words, inclination). If you release your edges without moving your CM down the hill, of course, your skis will just slip out from underneath you. So you must move downhill before, or as, you release your edges. And if the CM is not already moving downhill on a path that crosses the path of the skis, as it would be (or at least, as it should be) when turns are linked, then we must recruit some external force to push or pull it down the hill. That's simple physics.
In a traverse then, or just a standstill, we must do something to get that CM moving down the hill. It can be so subtle that we might not even notice it, but that something would generally be some sort of a lateral weight transfer--momentarily and microscopically extending the uphill leg or retracting the downhill leg--or it could even involve a push with the uphill pole, although that would be less likely. Simply angulating with the ankles, knees, or hips involves only internal muscular forces that move one thing one way and something else the other way, keeping the CM laterally undisturbed.
These things are absolutely necessary, required by the laws of physics (Newton's First Law--a body at rest will remain at rest until an external force acts on it...), and not debatable. But from a practical point of view, they may well be unnecessary to consider--as you suggest. Our bodies know very well how to do these things, without our conscious awareness, understanding, or direction. You don't have to remember, or even to know how you do it, to get your body moving forward from a standstill before you take a step forward with your feet. So your point that it's easy--just tip your feet, knees, or hips and release your edges--will work for the majority of students, because their bodies already know how to keep their balance. A little practice and coaching with sideslips--making sure that the shoulders don't tip up the hill as the edges release, for example--is all it takes for most people. Tip the feet to release and slip, tip them again to set the edges, repeat, repeat, repeat, and most will figure it out without needing to understand the underlying physics, and without necessarily needing to be reminded to move downhill as they release their edges.
Effective teaching does not always need to be 100% technically accurate in every detail. And 100% technically accurate, fully detailed explanation is not always (or almost ever) good, effective teaching. As Horst Abraham once asked, "does a butterfly flap its wings up and down, or does a butterfly just fly?"