The thing is that we can _measure_ radiation levels around nuclear power plants, with precision levels that are bordering on insane.

And the upper limits of possible exposures for the general public are well within the natural variability of the background levels. A person in Boulder, CO would receive more irradiation just due to higher levels of the cosmic rays than a person living next to Nine Mile Point power plant in NY.

So any possible cancers have to be caused by something else, and not by radiation exposure.