I think the military appreciates the security advantages of open source more than many other organizations. There's really no way to trust national security information to black-box proprietary systems. This concern has even extended to the actual chips running the software, since they're often made in China.
I always assumed the military would insist on having full sourcecode for everything they used, to protect against an important supplier going out of business and the like.
I'd be surprised if they didn't have access to all of the code for pretty much every Windows product for example.
The problem is support. If DoD actually do a source update to a supported software package, such as Windows XP, MS is not required to support that update. From what I understood, if its a security flaw, or major operational impact, they work with MS to fix it and that doesn't cause support problems to the same extent.