Nuclear energy may be safe, if done under near-perfect condition, with extremely large budgets to understand risks, and plans to mitigate incidents. There is truth to the argument that nuclear power saves lives compared to coal power.
But nuclear power isn't inherently safe. It is, by its very nature, extremely dangerous. Actual nuclear scientists understand that. See, for example, Feynman's work on nuclear safety during the Manhattan project.
Strapping a nuclear reactor to a rocket is almost by definition a dirty bomb. Depending on the height and mode of an eventual launch failure, the result could be anything from Tchernobyl to a less-dramatic yet more deadly dispersal of nuclear material in the upper atmosphere.
The dose-response relationship of radiation exposure is largely linear, meaning the latter event might just increase your risk of brain cancer by 0.005%. Yes, you may consider it negligible. But statistically, it would kill half a million people.
To blithely state that "nuclear is safe, hoho, why shouldn't we strap Plutonium to a rocket, you environmental nincompoops" has nothing to do with science, and gives science a bad name. Maybe NASA could come up with a way to protect a reactor during a missile launch. But it wouldn't be easy, and saying "why wouldn't we?" on TV would not inspire confidence in their abilities, but doubts in their sanity. The right thing to say on TV is "We're sending a reactor into space, and here are the mechanisms we've come up with to make it safe..."
