And yes, I know about dark fiber. Dark fiber networks don't have traffic but they're still on maps and have warning signs around them. There's a difference between burying fiber without using it and keeping the existence of fiber totally secret.
I guess I don't see how we could have a parallel internet whose existence was unclassified that no one noticed until now.
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.
Seriously, have you not heard of dark fiber? It's quite common for a network owner not to "light" many of the fibers in a particular run. Sometimes, this is because the capacity is not needed, but it's also common that the network owner's customers prefer to run their own multiplexers. Those customers could include the NSA or whatever agency in the government. Many such agencies certainly have built multiple classified networks this way.
Your average backhoe operator doesn't know what's in the pipe any more than the Dig-Rite spraypaint guy or even AT&T technicians do. The sign just says, "Buried Cable: Call Before Digging". Of course sometimes cables get cut anyway. That's why excavators get bonded. That's also why networks that aren't designed by "idiots" are redundant.