IS turns ON when video starts!
Magnetostriction is a bit of an odd phenomenon. To picture what's happening, think of a winding traversed by an electrical current. Whenever the current increases, the magnetic field pushing apart the individual strands in the winding increases, effectively minutely increasing the volume of the winding. When the current subsides, so does this mechanical force, allowing the winding to return to its relaxed state.
Now, the reason why there is a such high-frequency current variation in the said windings is related to electrical efficiency issues (preservation of precious battery power). A detailed explanation would be way beyond what seems appropriate here, so I'll simply suggest that you research the following topics if you want to dig further: Linear vs. Switched Mode Power Supplies, and Pulse-Width Modulation. Suffice it to say that it is more efficient to send a pulse train with a 50% duty cycle (50% of the time full ON, 50% of the time OFF) than to create a 50% amplitude constant current to drive a winding. The former uses less than half the power required for the latter, generally speaking, and the end result is identical.
So, the question is thus: we have tiny windings being fed high-frequency pulse trains. A corresponding vibration in the windings produces an audible sound in some cases and not others. Why? As it has been pointed out, the sound is, in the worst cases, really faint. I posit that the only reason it can be heard at all is because, when IS is OFF, the magnetostriction frequency is absolutely constant, and so is the resulting sound. When IS turns ON, the duty cycle (and/or frequency of the pulse train, depending on the strategy adopted by the designers) starts varying with the vibrations imparted on the camera (i.e. the IS goes to work). The faint sound is still there, but it is much harder to isolate because it varies constantly and randomly. In other words, it is much easier to train one's ear to a constant sound than to chase some ever-changing elusive whisper. There may also be some other electrical explanation (for example, a severe increase in pulse frequency when IS kicks in, moving the sound into the ultrasonic domain), but that would need to be verified in-circuit.
One could also speculate that there might be a resonance effect at work, effectively increasing the sound output when the frequency is constant and near a certain resonant frequency. But that would be pure speculation until resonance can be identified and demonstrated factually (and I would like to believe that such resonance would have been caught and eliminated by Olympus' engineers).