When he said "at a small base outside of the Hanscom U.S. Air Force Base" I took his responsibility to be that of one of these two bases (or perhaps the AOC if that was elsewhere). I'd agree that it seems unreasonable for a single person to have such responsibility, even for their 'ground' software. Operational battle management software would also probably come from a different place than the payroll systems, for example. The software in the various air platforms would likely come from each platform's development programme.

In the UK and Canadian military, there is no single overall software person, although there are technical authorities who define standards, etc, that should be used when software is developed.

FWIW, the UK Ministry of Defence actively supports the use of Commercial Off the Shelf (COTS) software. This isn't always OSS, but is at least better than building everything from scratch. A good ongoing example is the use of 'serious games' to support military training, e.g. as image generators inside simulators or as standalone desktop training packages. There are various COTS packages that fulfill both of these and other roles.

[EDIT: Typo]