Your quote is accurate, "direct access" is not verbatim. Though "collection directly" and "direct access" seem semantically the same to me in the context of the slide. [1]
The relevant slide is talking about two types of mechanisms the NSA analyst should use. The "Upstream" and "PRISM". It's within the the Prism description that the words "collection directly from the servers of.." is used. So it's not referring to raw data collection through neutral access points, as that's what the "Upstream" is. It's explicitly saying the NSA has direct access to these companies.
The relevant slide is talking about two types of mechanisms the NSA analyst should use. The "Upstream" and "PRISM". It's within the the Prism description that the words "collection directly from the servers of.." is used. So it's not referring to raw data collection through neutral access points, as that's what the "Upstream" is. It's explicitly saying the NSA has direct access to these companies.
[1] http://i.imgur.com/kIEtXjk.jpg