Let's say you had an arduous journey all the way down to the south pole. Once you arrive there you pull out a compass Which direction would it point, since every direction from this point is north?
The compass needle would point towards the south magnetic pole. (which doesn't coincide with the geographical south pole at 90 degrees south)
If you were directly above the south magnetic pole your compass wouldn't preferrentially point anywhere since the magnetic field lines would be vertical. (ie. there would be be zero force component on the compass needle in the horizontal plane.
You can get a compass which has a needle free to rotate on any direction ( on gimbals). The needle would always line itself up with the magnetic field lines no matter where you were on the surface of the Earth.
You have all made an implicit assumption about the word "compass".
There is no evidence to suggest XUD did not mean a compass ( or strictly speaking, a pair of compasses ) of the kind used for drawing circular arcs, etc.
In that case, the compass points in whichever direction the pointy bit is held.