Not quite, the military really only cares about the SIPRnet, a construct that is thankfully completely free of the likes of AT&T, the FCC, etc. The military has never depended on the Internet normal people use. Its a great service for Bob and Joe Servicemember to be able to watch Netflux in their down time, but because its not really important to any mission in any way, they dont care.
That's not really true, NIPRNet (unclassified regular Internet) is just as important nowadays.
There are a lot of essential communications going on that aren't classified, and not everyone doing an essential job function has a security clearance.
