In the video The Moon Trees That Flew To The Moon On Apollo 14 after about 08:47 Scott Manley says that Apollo 14 "flew up over the top" of the Van Allen radiation belts and simultaneously shows this retro-looking graphic of them.

Is this claim itself "over the top" or did the mission (or all Apollo missions) indeed fly up over the tops belts and avoid exposing the astronauts to the radiation trapped within them? Did the spacecraft do the same on the return trip as well?

So the trajectories that they took to the Moon flew up over the top of the belts, so that they minimized the dose.