In Arlington VA I take the bus every day. It's not only faster (it takes HOV on 395 which is 10x faster than the regular travel lanes), but I don't have to pay for parking either. The only better alternative I could use for commuting would be to ride my bike, but I really don't have a good solution for my suit.
WMATA has its huge flaws, but the buses are usually on schedule, clean, and safe.
Also a large portion of personnel working in that environment, even in the federal buildings are contractors. Only difference between that and this, is the location they're working. Which as you said, has to be vetted facility wise to meet the same standards as federal spaces.
I think you're really not giving enough credit to those in charge of security auditing in the DoD.
First, this may be the way the general likes to explain it, but I don't think it's entirely true, that their tactic is based on security through obscurity.
Second, I don't believe those in charge of the auditing would let something as simple as not having the right device to read an old floppy foil their intrusion attempt.
It may be old, but I'm willing to bet it's just as secure now as it ever was.