I've brought this point up a number of times during discussions when we discuss navigation near the poles. People generally misunderstand that the magnetic field lines are nearly vertical throughout the Antarctic and Arctic circles. The compass does not work in those areas, since the needle attempts to point downwards.
If you look at the
magnetic field lines on an illustration you'd notice that the lines are nearly vertical throughout the Arctic and Antarctic circles. It's actually only a relatively small strip of land where the compass works, near the warmer areas where everyone lives. Even at the altitude of Seattle Washington the compass is already scraping along the bottom of the dish.
That aside, there is
some controversy on whether Byrd truly flew over the pole.