Only makes sense, if you pay someone to manage your server...part of that is them making sure you have a recovery backup.
Also means, those top secret messages are still outside of our security apparatus’s controls for handling classified information.
A “spillage” of classified information usually requires the shutdown of any and all potential servers and devices attached to it. If there was classified info on the State Dept server, then it must be shut down until a though inspection is made to it and all PCs on that network.