If I think of the neural hash applied to government the obvious use is that one would make a database of classified photographs and images.

If somebody had those and wasn't supposed to have them than that would be a basis for action.

Other than that I don't know what set of images you'd be concerned that government employees had, but if you did have something that "went viral" in some way you could trace where it went.

In general you should look at the methods that are used to verify nuclear weapons disarmament. There is a big literature on this: the US and Soviet Union have all kinds of methods they use to prove that they are conformant with arms agreements while keeping as many secrets as possible.

That kind of thinking could be applied to other domains.