Ah, so it's confusion about how classification works.
Information gets classified, not documents. A document with a classification marking on it has it because it contains information that has been classified. They weren't attaching documents previously stamped "TOP SECRET" to their emails. They were emailing like normal people do, and because of the nature of their jobs some of their discussions ended up including some information that had either already been classified or (for most of it) was retroactively classified after they discussed it via email. The way this worked is likely the way any email chain worked, it began about something that wasn't classified (so the subject in the email header didn't contain a classification marking), maybe a call she was scheduled to have with another country's ambassador, and then someone mentioned something that was or became classified. E.g.:
Aide: "Mrs. Clinton, don't forget you've got a 10:30 call with the Japanese ambassador."
Hillary: "Thanks. What are the main things we discussed wanting to focus on in that call again?"
Aide: "A, B, C, D, E."
And C was or included some information that was classified.
There are nearly infinite ways this could've happened without anything that might be reasonably characterized as recklessness or ill intent. That is actually the real danger of maintaining a private server for email: even if everyone involved is brilliant and extremely competent, it's still pretty much impossible to guard against inadvertent disclosure of classified information in a setting that isn't secured.
And I'm done with this tangent. I don't even really like Hillary at all, but I think it's important for people to understand how much of the information even non-Trumpers buy into about her (and often, by extension, Democrats more generally) is just wrong.
ETA: I just figured it out! Sawbonz still has to use fax for work, he's probably never even sent an email. Understandable mistake.