Vs. Wikipedia says the entire U.S. Army (active duty) has ~485,000 personnel.
Divide...and that's ~0.17 Army people per acre, even if the US Army had NO job except holding down the NTTR. (Which is actually US Air Force, BTW.)
[Edit: But +1 - because in the bigger picture you make a valid point. However vast the open spaces, at the spots where the cool & expensive stuff sits, there does have to be some sort of "real" security. If only so dodgy locals don't swing by with a pair of bolt cutters, and start helping themselves.]