That is not a robust statement.
For instance, the one ski skiing here
Is certainly skiing, but lacks inside ski tipping.
Isn't using inside ski tipping to promote or drive outside ski engagement.
While this is now quite old, Paerson here,
likewise isn't using the inside ski in this manner, though she does lift the new inside ski at the end of the segment.
I think each of these three skiers (actually 4, there are two demo-ers in the Burke video), though they may fall short of the lofty standards of some, are pretty good. How can they perform at their level if they are not displaying one of the fundamental movements of skiing, not in just one turn, but turn after turn after turn?
The movement pattern BTS is pushing as "fundamental" does happen in racing, but not in the majority of turns. However, racers are great carvers, great skidders, and all in all great skiers. How can a movement be fundamental if it is missing from the majority of turns of some of the leading demonstrations of ability of the sport?
Now, what using inside ski tipping to drive outside ski engagement does do, depends on the sequence, but: if you let the pressure run out onto the old inside (uphill) ski so that the outside edge of that ski is weighted (and weighted more towards the tail) then tip the new inside ski, you get a sequential release, with the new outside (still uphill) ski then rolling onto the inside edge kinda smoothly. And hoepfully you also got forward at the same time. Neat trick, one good way to show people how to use the sidecut of a ski at an early level, and in the context of letting the turn run out to carry speed while still edging there's even a specialized German phrase for it. But, there are lots of specialized German phrases in skiing that aren't used in every turn.
For me, I prefer robust concepts, so would hesitate to characterize as "fundamental" something that certainly works, but isn't needed at all to ski. Hop turns are another good example. They are good drills, of one sort, even today, and you can ski using them, but you can also ski very well without using them.
Socially, however, the movement pattern BTS describes is in some ways a group identifier, and so it may serve other purposes beyond the task-related ones involving on-snow movements.