Other ways you could defeat this:
- Take a picture of the screen with your camera phone. Yes, they don't allow camera phones, but you could probably smuggle one in. This obviously doesn't work with anything that's too long.
It would really be pretty hard to do this so it can't be compromised by a motivated attacker. Impossible? If you consider that the system can't be so locked-down no one can work on it, perhaps yes.
Really the hardest part of doing this, now that I'm thinking about it, would be the "hex dump" step. Once you've installed the equivalent of a hex dumper -- some way, some how -- you can manipulate that hex however you want to get it past the proxy. After you can dump the secret data to hex, it's game over.