This item makes me wonder what instructors are taught and what they discover through attention to detail when flying.
As part of a prestart up check the instruments are checked for damage and serviceability which includes the Altimeter and VSI.
Is it not part of the routine to zero the altimeter? I'm sure it is or ought to be. The engine and rotors are started and if you are attentive with your after start checks you will notice that the reading on the altimeter has changed, it now shows a minus altitude (the pressure under the rotor disc has increased). You are unlikely to see any change in the VSI as the indication of RoD (Rate of Descent) will occur quickly.
Lifting off into a low hover will further increase the pressure under the disc and a further minus altitude will be indicated. Move forward and at about the same time as you loose ground effect and gain translational lift the altimeter will show the actual height and as you climb away the altimeter will operate as you would expect.
In the descent is it not reasonable to expect some reversal of this occurrence?
The VSI reacts to pressure change over time. The time involved in the final part of an approach is short and the pressure change is rapid, hence the VSI indication. The fact that the static port is under a cowling will not change the situation. Pressure change is pressure change!
If you really want to be a bastard, why don't you chase your student for miss setting the altimeter, as it shows an error when hovering.