To be honest, I though mutants being wrongly hauled around by crazed soldier types was just some sort of inevitability in comic books involving mutants... and, I doubt it really is the government involved since that’s way too vague and impersonal of an enemy for the show, I think it’s someone (probably someone we’ve already met) taking advantage of Nathan so they can use government resources, and by and large, the government doesn’t know what’s really going on.
The government does know since Nathan references getting orders from the president.