Imagine, if you will, living somewhat close to a nuclear reactor—not right next door, but close enough—and then imagine that an accident at that reactor causes a large release of radioactive isotopes into the atmosphere. Certainly scary, but maybe less scary because you know your government has computer models that show where the nuclear fallout will blow and fall, and they explain that the amounts that will blow and fall on you are negligible.
Sure, you might think twice about that reassurance, but it is not like they are saying everything is OK. The government, after all, did evacuate some people based on their fallout models. . . so they are on top of it.