You want me to speculate about arrow direction?! alright, generally speaking the access is not "direct" because the "boxes" act as buffers. I can't say if they "pull" the boxes or they just serve subpoenas to them and get the data pushed back.
Quite the opposite - no speculation is required. The NSA has direct access. Any discussion that focuses on how is a discussion of semantics, and as such is of anecdotal interest.