The issue of inside vs outside ski for a skier is very similar to front vs rear wheels for bikes/cars.
On a bicycle, braking forces on the contact patch between the tire and road are positioned well below the rider's centre of mass, thus produce a torque around the transverse axis that tend to tip the rider forward, transferring balance to the front wheel. This happens regardless whether the initial braking force is generated by the front or rear wheel. If braking with the front wheel, more and more pressure transfers to the front wheel, increasing friction, thus brake force can increase to the point that the bike completely tips over (a "stoppie" or "endo"). If braking with the rear wheel, you'll eventually reach an equilibrium where the pressure and thus grip is reduced by the balance transfer, no additional braking force between ground and rear tire can be generated, and you just gently skid. Which is why braking with the rear wheel is "easy" but, for high performance riding, ineffective.
Similarly for skiers, lateral forces produce a transfer of balance from the inside to outside ski, thus extreme turning forces can only be generated by the outside ski, and begintermediates who ride the inside ski end up gently skidding (which they are usually fine with).
The key is to understand that the transfer of balance is the RESULT (output) of generated braking/turning forces, not so much the precursor (input).