OK, more info: pressing on the unit does not lower the noise, it's changing its orientation that does it. The noise gets progressively louder tilting the unit along the pitch, gets progressively quieter as I turn the unit along the roll axis. Yaw makes no difference (so, hey, gravity not magnetic I guess).
My guess is the disk is unbalanced. I had discarded that when I thought I could press down to reduce the vibration but since that's not the case...
So: not a vibration then but the actual whirring of the disk in space? I assume I cannot do anything about that. Boo. But I'm still not quite sure why that would vary with pitch and roll. Maybe the moved air finds a better path to circulate in some alignments?
Note that I have always had the unit stacked (on a desk, under a screen) but I isolated it for the test.