Your fallacy is assuming that classified information only exists on classified systems. In fact, "classified" information pops up in all sorts of places: conversations, personal observations, news stories, etc. Did you know that we use armed drones to strike terrorist targets? Congratulations! You know "classified" information, and nobody bridged the gap between a secure system and you. Similarly, if I sent you the NYT article about the drone program, the CIA would assert your mailbox contains a Top Secret document. Asinine? Yes, it is, but that's the way it works.
But most of Clinton's "classified" email wasn't even that juicy. It was routine correspondance from foreign sources. Such correspondance is considered automatically classified, regardless of content. If Angela Merkle sent Clinton a note saying she expected nice weather for her visit, voila! Clinton's "classified" email count just increased by one.
Be clear, I am NOT saying all of Clinton's "classified" emails fall into those categories. The overwhelming majority do, however, as you can verify for yourself if you care to read them. The open question is about the handful that have been wholly withheld. We simply don't know about them.