Executive summary: Apollo used trajectories above and below the highest-radiation areas of the belts, and traversed them pretty quickly. All of the astronauts wore dosimeters. The total radiation received was in the 0.5 rad neighborhood, except for Apollo 14, which received 1.15 rad. Nasa's tolerable limit was 400 rads whole-body and 50 rads to blood-forming organs.
Still, a certain amount of luck was involved. A very strong solar storm could have caused problems or even killed the astronauts.
There is only one problem with the “readings”.
The Belts they allegedly passed through were a lot smaller than we now know to be true.
The fakers did not have the current data.
Oops.
This will stop being a debate and become a real world problem for Elon Musk soon enough—when real astronauts have to pass through real radiation.
Name call all you wish—we will know for certain soon enough.