When scientists speak of radiation, they speak not only of single doses but also of cumulative doses.
See for example, this research from the University of Iowa showing that “cumulative radon exposure is a significant risk factor for lung cancer in women”.
And see these studies on the health effects cumulative doses of radioactive cesium. (As I noted on March 29th, the radioactive cesium fallout from Japan already rivals Chernobyl. And the amount of radioactive fuel at Fukushima dwarfs Chernobyl).
Admittedly, the damage from huge single doses may be greater than the same cumulative dose from many small exposures. But the smaller doses can still add up.
Many studies have shown that repeated exposures to low levels of ionizing radiation from CT scans and x-rays can cause cancer.