I think you are missing part of the irony here. A good number of those Hillary emails should have been on a government server in the first place, signed for entirety by the government for archival. Non-repudiation is an explicit design goal for the communication of public officials.
I think you're confused. Very few Clinton emails were ever leaked or released. The major leak people like to talk about was of John Podesta's emails. Podesta was a private employee of the Clinton campaign, he never worked at the state department. And of course being the campaign manager, having his email be provided by a government agency would have been a huge campaign finance violation to begin with.
