The term "base" used with data would correlate well with the military term for "base" and perhaps adds some color to its original context.
Perhaps a "data base" originated as "A safe refuge of facts from which you would learn, train, and launch a defense or an attack?"
Or perhaps its a "base" (basis) of facts from which you operate in a military operation?
Or perhaps someone else non-military used the term first but it picked up early resonance in the military community due to its additional connotations for them or their management?
Anyway, TIL. I wonder whether a FOIA request to NSA or DoD would turn up anything.