For the servers outside, the case that happened in Greece after the Olympic games as an example of something much, much bigger but conceptually still more an immense "wrench" than a "cryptanalytic" approach:
I always considered the "crypto nerd's imagination" panel in the comic to be that the NSA have computational and/or cryptanalysis breakthroughs and super computers so far ahead of anyone else that they can crack almost anything. My guess is that in reality things are much plainer and they can rely on cooperation and server hacks.
They very well may. For all we know, some of the Snowden revelations are distractions from some breakthrough, designed to protect the real secrets.
The scale out of the NSA capabilities may have become an issue -- adversaries have figured out that the US knows too much, as people get blown up when they pick up the phone.
https://xkcd.com/538/