There are no secrets in a legal sense e.g. NDAs. However, there is a culture around private nuclear labs of giving no hint of their existence so that they can hide in plain sight.
The objective is to avoid attention, not to be secret per se, though the effect can be similar.
Here in Toronto, every once in a while, someone has a meltdown (if you'll forgive the expression) when they rediscover that there is a CANDU nuclear fuel manufacturing plant in their dense and quiet suburb.
Now CANDU reactors run on natural uranium. So they're forming metal pellets out of uranium powder. The main risk is direct chemical toxicity from the uranium, not the radiation. But for many people "nuclear fuel" might as well mean hot nuclear waste.
The mystical level of dread it inspires in some is hard to overstate. Just to avoid drama from the neighbours it's understandable they try to keep quiet.
The objective is to avoid attention, not to be secret per se, though the effect can be similar.