The time spent in the radiation belts was very short(time and exposure factors) and the radiation particles are widely dispersed in a way that there were few particles per given square cm’s that could actually do much damage. So yes the Van Allen belts have highly energetic particles but they aren’t concentrated in a dangerous way that say a gram of plutonium would be if held in one’s hands. The capsules did have decent shielding.
That is the “story”, but current scientists are working on a way to store water in the outer shell of the newest capsule to shield it. That is a lot of extra weight, if it isn’t important. They are also deciding how many boosters have to be in orbit to refuel, and having them in orbit around the Moon too. To me that means, it never happened. Plus the proven fake pictures of Earth taken from halfway to the Moon, with some camera tricks.