The system of radiological protection has been based on linear no-threshold theory and related dose-response models for health detriment (in part related to cancer induction) by ionizing radiation exposure for almost 70 y. The indicated system unintentionally promotes radiation phobia, which has harmed many in relationship to the Fukushima nuclear accident evacuations and led to some abortions following the Chernobyl nuclear accident. Linear no-threshold model users (mainly epidemiologists) imply that they can reliably assess the cancer excess relative risk (likely none) associated with tens or hundreds of nanogray (nGy) radiation doses to an organ (e.g., bone marrow); for 1,000 nGy, the excess relative risk is 1,000 times larger than that for 1 nGy. They are currently permitted this unscientific view (ignoring evolution-related natural defenses) because of the misinforming procedures used in data analyses of which many radiation experts are not aware. One such procedure is the intentional and unscientific vanishing of the excess relative risk uncertainty as radiation dose decreases toward assigned dose zero (for natural background radiation exposure). The main focus of this forum article is on correcting the serious error of discarding risk uncertainty and the impact of the correction. The result is that the last defense of the current system of radiological protection relying on linear no-threshold theory (i.e., epidemiologic studies implied findings of harm from very low doses) goes away. A revised system is therefore needed.