Yes, the dangers from the pursuit of nuclear energy are exaggerated, because nuclear energy is on the whole safe. People who do not like nuclear energy because they have an environmental agenda to reverse progress want people to think that it is not safe, but this is only because they want to project their values on other people.
As we know from disasters like Chernobyl or more recently Fukushima, nuclear energy can be extremely dangerous. In the event of an accident or catastrophe, nuclear waste cannot easily be contained and instead leaks out into the environment where it wreaks havoc. It does not quickly dissipate but rather lingers and does it damage for many, many years. Morbidity and mortality can be high and in the event of a real, uncontained accident could be catastrophic.