Here are some other wild guesses that may have little or no resemblance to what Verizon is experiencing, but kind of show what can bring down an Internet-like network:
* Some sort of configuration fat-finger that got rolled out everywhere without proper testing. You'd like to think that's impossible on this scale, but after having an insider's look at the operations of a couple major US cable companies, I put nothing past telecoms.
* Verizon probably runs some form of routing protocol internally. If a core router has gone insane, you could, conceivably, get route flapping and bring down pretty much everything, but that's not supposed to happen on carrier-grade equipment (cough see previous paragraph).
* In a closely related scenario, large portions of the public Internet have been brought to their knees at least once by a nasty BGP bug in a major vendor's routers that got triggered when somebody broadcast just the right set of options in their announcement. Picture a guy in upstate New York trying to route around a bad line card, and suddenly the US goes dark because half the routers crash when they got the BGP table update.
You can probably spot a common theme here -- a "decentralized" but homogenous network is still vulnerable to the triggering of problems shared by all points.