It is extremely possible for a junior enlisted soldier to access and download classified information in the way that has been suggested. People claiming otherwise in this thread keep talking about their time in SCIFs and how that would never happen in a SCIF. If they actually had the experience they claim they do, they would remember that a SCIF is called that because it stores SCI, not secret. You do not need a SCIF to store secret material. By definition secret material is secured at a lower standard.
This will undoubtedly get me flamed, but what happened is 100% the result of Bush-era intelligence policies. EVERYTHING is classified now. Because of that, hundreds of thousands of soldiers have security clearances and access to classified information in their day-to-day jobs. The attitude of many, many people in the armed forces is “oh, it's only secret, it's no big deal.” And that is a recipe for exactly what happened in this case.
Actually, you were not flamed. And from what I have seen over the last few days since your post you were pretty much on the money. Good post!