The evidence of safety isn't the issue it's that nuclear accidents however rare have huge implications so stick in people's minds. We're bad, mentally, at appreciating low level dangers that are diffuse like minor pollutants which kill slowly or degrade people's health over time. What does stick in our minds well are singular big events like terror attacks, Chernobyl or Deep Water Horizon.

Even our legal systems address singular events better than low level harms because it's harder to deflect blame because the damages are so immediately identifiable; Fukushima and Chernobyl destroyed their closest cities and areas overnight in ways that they'll likely never recover from and the effects of their poisons are rapidly identifiable.