As a member of the military who has no fear of asking logical questions of his superiors, I asked my Communications Officer why this "ban" was being instated (it hadn't been instated at the time). The answer I recieved was that it was against the UCMJ to look at the material.
 
That answer is a gross over simplification of the truth, but it is essentially true. As a member of the armed forces, we are required to safeguard the secrets of the United States and prevent their dissemination. Therefore the simple act of viewing one of those documents in a non-secure manner without need to know represents a security spillage, and is essentially against the UCMJ.
 
As to the *reasoning* behind this, honestly? It probably has more to do with keeping DoD computers free of this material than keeping DoD employee's minds frees of this material. The .gov is trying to limit the spillage as much as possible. Doing a proper scrub is an incredibly costly and time consuming process, now multiply that across the hundreds of thousands of computers owned by the DoD... All of us soldiers and sailors and marines and airmen know exactly what's going on over there, spilled documents or not.