If the two "independent" coils are each wound on gap-less high permeability cores then coupling is greatly reduced. The problem arises when the core material is low permeability or, (as in the case of a lot of inductors), there is a significant air-gap. This is because the magnetic field "fringes" due to air carrying the flux. Air is a poor concentrator of flux and coupling can happen because the lines of flux "spread-out".
The coupling also depends on operating frequency. Induced voltage is N\$\dfrac{d\phi}{dt}\$ and the rate of change of flux is proportional to frequency. However, flux is also dependent on the ampere-turns in the "transmitting" coil and as frequency rises (for a fixed inductance value), current falls proportionally.
There comes a frequency (and this is beyond my memory at the moment) where the choice of "protection" changes from using high permeability material to using a solid conductor between the coils. At low frequencies, the high permeability material allows flux to be taken away from a sensitive "area" and return it back to the original source; in effect the fringing that splays out from the "rogue" field is kind of short circuited by a low reluctance path that bridges north and south.
At higher frequencies solid copper (or even silver) conductor sheets become more effective and you see this type of thing in radios - a square shaped can sits over an inductor. Why does mu metal get worse at higher frequencies - mu metal's "effective" permeability reduces with frequency (due to eddy currents increasing) and it becomes less effective as frequency increases. The two effects tend to cancel but, because mu metal is a relatively poor conductor (compared to Cu) it doesn't do the job that a good Cu conductor does at high frequencies - the eddy currents induced in copper are many times that produced in (say for instance) iron or mu metal.
Where do you pitch the protection - both can be the best solution but one may be just as good as both if the frequency is low or high.
