In fact, exposing classified information can be a bit bad for one's career.
Once took a computer service call at one of the Lockheed Skunk Works buildings. Up in Burbank somewhere, I think. They had a sign on the Emergency Exit door in the lobby. Basically said - Unauthorized use of this door by an employee during a non-emergency will result in the termination of the employee. Did not even ask what they meant by termination. Assuming job loss, but after seeing that, I thought, these guys is serious.