From its countdown server to the video streams behind NASA TV, NASA runs a lot of Fedora (and Red Hat Enterprise Linux), as Jack Aboutboul was privileged to see on a recent tour of NASA's facilities in Jacksonville, Florida.
I suppose it's not surprising that an organization like NASA would use free software like Fedora, in addition to its commercial cousin, RHEL. After all, NASA is powered by rocket scientists (pun intended) that want maximum control over their IT. Fedora gives that to them. No, they don't get commercial support for it, but they likely don't want it, either.
There are some things for which organizations are best positioned to self-support. For everything else, there's commercial open source.