> The DNC could have simply published one of their original emails for people to compare, without interfering in any investigation or revealing any spy techniques.

Ok the DNC goes to their hard drive and opens up the email. It does not match what was in the leak. Is the email on the DNC's hard drive altered or not? After all if the email was accessed/leaked could it have been altered as well? With a simple security setup, yes it can.

Operational security is often about not tipping your hand to your adversary about what you know and what you do not know. Showing the original email in your scenario also tips your hand for what you think you know.