Well, the gradient coils do move (albeit very slightly) because of the enormous forces generated by the interaction of the static and dynamic fields - it's difficult to hold the wires still, as there could potentially be several hundred lbs of force. It's this movement that generates the noise. Simply altering the magnetic field doesn't produce the noise - it's the forces on the wires.
The same thing explains the noise that switching power supplies make - the ripple current in the magnetic components constantly varies, resulting in oscillating magnetic forces in the inductors, which can cause loosly wound coils to vibrate. In the case of PC VRMs, an audible vibration is likely to come from a subharmonic oscillation (maybe mechanical) as the operating frequency is typically in the MHz range.