And the government is welcome to investigate. But they can't compel a third party to help them conduct the investigation just because it would be easier on them.

I doubt there's a legal basis for saying that these "alt_X" accounts are functioning in the role of a federal worker. They're obviously not advocating the official government position -- that's the whole point of them. They clearly state they aren't reflective of the views of the agency they're referencing. You'd effectively be arguing that no government employee could ever, in any capacity, express an opinion related to the function of their agency.