Well, I guess it depends on your definition. When I worked in telcom we called it "dark fiber" if the multiplexers at each end were operated by someone other than the owner of the fiber. This was "dark" in that the network owner didn't know anything about it besides who had access to the server closet in the CO.

The point is that the USA government leases a great deal of network capacity, both directly and indirectly through "cover" entities. Much of that is probably used to build any number of networks that carry "classified" data, including SIPRNet, NSANet, JWICS, and others so "dark" that we don't technically know they exist. Nobody would bother to deny the existence of these, nor the obvious fact that the actual fiber belongs to the same firms that own all other long-distance fiber: ATT, L3, XO, VZN, etc.

I suppose it's possible that some agencies operate the sort of "secret network" you were challenging, but since it costs at least ten times normal prices for spooks to do anything, they probably try to keep that self-built stuff to a minimum.

EDIT: Just so we're clear, the security of a network does not depend on no one knowing it exists or where it is. The NSA knows encryption: no one is going to "tap" their fiber and find out their deep dark secrets. A well-informed goat enthusiast with a backhoe could conduct a denial-of-service attack, but that doesn't scale and as I said these networks have redundancy built in.