The "danger" of nuclear power is not their day-to-day operations, it is the nature of the waste product (both in terms of its decay to safe levels and the ongoing storage requirements) and the use of said waste materials in the relatively simple production of "dirty bombs" that just require standard explosives to distribute said radioactive waste around a large area.

So the danger is not overstated, it's that the promoters of nuclear energy refuse to accept the complete lifecycle of nuclear power, including both the fuel generation (uranium mining is environmentally damaging, leaving tailings and polluted water), fuel management (moving radioactive fuel around the community/environment), and fuel disposal (unsolved).