It is complicated, indeed. You've made a mistake too. The North Pole (geographic) of the Earth is actually the South pole of the Earth magnet (that's why the North arrow of the compass is attracted to that direction along the magnetic lines). So, the pointy end of a needle must go to the right on your image.



The problem with the screw rule is that people don't understand the whole picture - how the magnetic field line in particular point of space is forming a closed loop.

Anyhow, it seems to me that if a person is Okay with the simple logic and knows the Maxwell's rule, he/she will figure out what to do with all of that stuff eventually