"Collection directly from the servers of these U.S. Service Providers..." could easily mean "We ask them for the data and they give it to us from their servers."
Especially in the context of that slide where they are contrasting it with their "upstream" collection which would require sorting out the packets (and presumably decrypting them) before analyzing the data.
The slide with the explicit formulation in published today:
"Collection directly from the servers of these U.S. Service Providers: Microsoft, Yahoo, Google, Facebook, Paltalk, AOL, Skype, YouTube, Apple."
This supports the claims of Glenn Greenwald's article and is exactly what companies claimed not existing.