That is a good guess - the Home Subscriber Server is the authentication server in an LTE network. Short of this or a PCRF (Policy Server), I cannot think of any other single element that could bring the network down. Routing (as identified by another reply) could be an issue, but I would assume that 3G and 4G data use the same core network.

I have a feeling it might be the routing to the hss/pcrf that could have been the isue. Almost every carrier has redundancy for these products and they are often in geographically distinct areas. Perhaps the routing from the eNodeBs/edge network to the core network was handled by another division within Verizon or even leased from a third party and could have caused all of this

Or a disgruntled employee left a cron job on all the key systems to rm -rf :-)