"And, we take these people, and eventually - they'll build the next stock exchange, or 911 system, or flight control system on a large passenger aircraft..." What could possibly go wrong?

With the exception of a few government jobs and higher management promotions you probably won't notice much difference. To make things easier with getting an interview you might want to get certified in whatever your dream job mentions in its description. That said, you should consider using your psychology degree to your advantage. Your diploma coupled with any IT security certification will open many cybersecurty doors. Social engineering detection and data leak prevention are just two examples.