So, if your balance point is over the outside ski, then let's see what happens in each case.
OLR: You've removed the support holding your CM from crossing over. Resut: The CM crosses over.
ILE: You've raised the CM, moving the balance point from being over the outside ski to downhill of the outside ski. ie. outside of the base of support. Result: the CM crosses over.
In both cases you disrupt the equilibrium you have set up that keeps you in balance over the downhill ski. Note carefully, that the ILE is not pushing the CM downhill. It's just influencing the balance point. They are very distinct movements, that use the physics of the turn in different ways.