That is a rhetorical tactic that kind of misses the point - it's not that weapons reactors produce fundamentally leakier waste than civilian reactors, it's that the military has a long history of not disposing of dangerous chemicals the right way. It happens with non-radioactive toxic waste too and a lot of bases and the areas around them are contaminated.
If you want to use this as an argument for the safety of nuclear waste disposal, you would have to explain why the armed force's problems with waste disposal are specific to them and will never spread to regulated private industry. (P.S. the history of that is not great either and you might end up arguing that something which has already happened never will.)