What I think is missing in the public discussion of these sites is the communications infrastructure. A big bag of bits in Oregon or Nevada is not useful per se. They need to have very, very fat pipes effectively to everywhere (certainly everywhere Apple's customers are).
You didn't make notice of Facebook's data center being in the above picture also. That's one reason why Apple plopped another one down "across the street". There already is major redundant cable going through the area.
Likely same issue for the Nevada site. There are a couple of higher profile CA based companies that put back-up/expansion sites out near Reno ( just couple hour drive up I-80 from SF Bay Area ).
They used parallel scale - they would locate what amounted to a NAS at a number of nexuses around the country. When you went to fetch the content, you'd be directed to the topologically closest one.
For relatively static contact that works fine. Apple outsources that for purely static stuff.
So what does Apple do instead? I imagine a non-trivial percentage of their traffic at this point goes straight to the wireless providers (all of those app and music downloads, push notifications, FaceTime setup messages, etc).
Push notification probably not. In order to route that you need personal account information. If the push notification is going to the Mac and iPhone it is not particularly likely they are both on the same cell service backbone.
Likewise for Facetime set-up.
Music is static data. There is nothing unique about which different users having access to the same song. Apple could replicate their whole catalog at different ISP's and cell backhaul network centers. (or outsource it). The locations are dynamic but shipping a customized URI to the data isn't a major bandwidth problem. It is the actual content that chokes the pipes.
Do these data centers just have a big fiber link to Verizon and AT&T? To where else do they directly connect and how?
These data centers serve users worldwide. You're thinking too small. It is the major Internet backbone vendors Apple needs connectivity to. It is short hop connectivity to Tier 1 Internet backbone providers that is important.
For Oregon is more likely that Century Link ( Qwest) is the larger major "pipe" running through that area. There are portions of Verizon and AT&T that are tier 1 providers but they aren't the only (or biggest in Verizon's case) ones.
http://en.wikipedia.org/wiki/Tier_1_network#List_of_tier_1_networks
In fact you actually would
not want all of these data centers on the same Internet backbone provider. Ideally would have a different pair coming into each center.