I think Medium goes off the tracks just a little here. I want to point out a couple of obvious things.

1. Prism is not necessarily the only way they get data. There is nothing ruling out having an expedited system of getting requests sent, and having some sort of access.

2. "Directly from the servers of...." can only be reasonably read one way. There is no reasonable reading of the slide which puts it in line with the NYT story.

I think it is therefore necessary to note three possibilities:

1. The NYT story is wrong.

2. The slide author was wrong.

3. NSA uses both these methods.