I don't know of a good oral history of PGP, but I suspect if you find one, it'll have the answers that you're looking for.
For unclassified systems, of course those are connected to the Internet. How else would you communicate with the rest of the world? And I filled out an SF-86 when I applied to be hired by them. There's nothing classified on an SF-86. No classified data was leaked when OPM was hit by Chinese hackers that stole all sorts of PII data for everyone who held a security clearance, including fingerprints and retina prints. Oh, and OPM was hit by the Chinese not once, but twice.
For classified systems, those are connected to the SIPRnet or other classified "internet". And those classified internets are typically shared with other governmental agencies, and not unique to DoD.
As to why mail servers hold email? That's how they, namely IMAP or EAS, work. If the mail server didn't have the mail, and the authorized user wanted the mail, where is it meant to come from?
The more pertinent question is: Why was a DoD mail server connected to the public internet? The DoD have their own network.