I think the Navy AD said it best... its about "optics". Perception is everything. Although private funds may pay for the team to travel and all the other stuff we have seen in the news articles, there are still DoD funds used, as little as they might be. Although they may have nothing to do with the game directly, professors are furloughed. Is the Academic Dean? He isn't needed for a football game, but I imagine he attends games along with the Supt, Dant, Dep Dant, and AD. Are all the trainers NAAA employees or are some paid with other money? Are there some football coaches who also teach some PE classes (pretty standard at Navy, you will often hear of a coach with tenure... I know all for teaching 1 PE class... ridiculous) for extra pay. So in some ways they are furloughed too. The USNA police force... I imagine they are working, but probably not pulling overtime. All that extra traffic and personnel on the yard probably requires extra shifts. I read yesterday that the USAFA Football Sports Information Director was furloughed. What about Navy's? These guys work incredibly hard and with a game that has that many viewers and with the extra media coverage, how would this all be handled? A lot of this seems minor and trivial, but there is so much that goes into putting games on, never mind Navy vs. Air Force. Even if NAAA, Air Force (not sure what their sports thing is called), and CBS offer to pick up the slack to include paying with private funds for furloughed employees, staff, etc (I suppose they would be individual contract employees to NAAA at that point).
Most of all its a perception thing. It sucks, but who can complain when people aren't getting pay checks.