A commercial vendor works to please large customers, such as the military. If the big customer needs a feature supported long term (remember that military systems commonly last decades), the vendor makes it happen. If the big customer needs a specific enhancement or fix, that is a priority for the vendor, and if it's needed ASAP, that can happen too.
FOSS communities are a bit more independent-minded (which I generally like) and some developers won't want to help the military for ideological reasons. Communication with FOSS communities is much different than communication with commercial vendors, and much less efficient.
I think DoD needs access to paid, professional developers who can provide those services for FOSS. That could be someone like Red Hat, it could be outside consultants, it could be internal developers, they could hire members of the FOSS community. Also, DoD will need to fork projects when the community is uninterested in a DoD priority.
And there's another major problem: Imagine bombs are falling, people are dying, national security priorities are being lost - and the military needs a fix or enhancement now. Submit a bug to bugzilla and wait? Email the dev list? IRC? They need someone to call, who can answer the phone and get things done.