It appears that low doses of radiation are not harmful, since the body already has methods of defense. Only after a certain threshold, radiation begins to harm the body. More than that, low doses of radiation seem to start the genes responsible with the protection against cancer, therefore the number of cases of cancer in regions with higher than normal background radiation is actually lower.
Of course, it was normal for people to fear radiation during the Cold War and now, as our fossil fuel reserves are close to depletion, nuclear energy is something desperately needed to compensate. How much of this documentary was actually about dispelling the exaggerated fear of radiation and how much was about promoting nuclear power is for you to decide.