Radiation takes a long time to build up damage when it's relatively weak. Astronauts simply weren't on the moon long enough, couple weeks or even a couple months won't be very much to worry about, if they started living there for years on a moon base or something then radiation needs to be taken very seriously. One reason why Musk's Mars plans won't work.

The real dangerous places in the Solar System for radiation are actually the Galilean moons. They're right in a Van Allen belt and deadly exposure is reached in a few hours or days depending on which moon you are on. Why that retard with the Europa colony idea can be dismissed outright when they act dumbfounded at the idea that your astronauts will literally drop dead day 2 into the mission.