The equipment for recycling used-up fuel rods is the same for creating nuclear weapon payloads. Governments struggle stomaching proliferation risk in the name of fuel efficiency.
That's mostly just fear mongering because mitigating that risk with organization and a little bit of planning is trivial. Just put the reactors and the fuel reprocessing in different sites under control of different organizations. To produce plutonium usable for nuclear weapons you need to pull the fuel out of the reactor way ahead of schedule for power generation. The longer you keep the fuel in the reactor, the more Pu-240 you produce alongside the Pu-239 and you can't make nuclear weapons with that.
Weapons grade plutonium requires very low concentrations of Pu-240 and that requires running the reactor specifically for this. If the reactor and fuel reprocessing are done by different organizations, then neither can make nuclear weapons without the cooperation of the other.
Managing risk with organization structure is a technique well known to virtually all governments, from western democracies to the worst dictatorships, so this isn't breaking any new ground.
