Not quite true, the mechanisms are quite different. Materials with high permeability are good for shieldning mainly because of their domain structure which "adapts" to resist being lined up when it is exposed to an external field, i.e. it is not a question about inducing currents as in the case of a Faraday cage. The reason why these materials do not work at high frequencies (above a 1 MHz or so) is simply that the domains are too "slow" and can't keep up.
In demanding applications it is therefore neccesary to combine many types of shields that work well in different frequency ranges, one should preferably also use several layers of mu-metal separated by spacers. I often use two-layer mu-metal shields as the first room-temperature layer (followed by other shield, including two layers of superconductors) and as far as I remember the shielding factor for two 0.5 mm layers of "standard" mu-metal is something like 10 000 at low frequencies (up to 100 kHz or so).
Also, even if there are opening is the shield it is still possible to get a reasonably good magnetic shielding factor. The "trick" is simply to keep the openings as far away as possible from whatever you are trying to measure. Magnetic shields are often made in the form of cylinders open at one end only, and as long as the distance between opening and whatever you are trying to measure is a more than 2-3 times the diameter of the cylinder it will still shield quite well at low frequencies (note that this does NOT work at high frequencies, then you DO have to close all openings).
(despite my rather embarrasing misstake above, I do have quite a lot of practical experience with magnetic shielding since I spent several years working with dc-SQUIDs).
