The term direct access was first used by the Guardian in their original story: "but the Prism program allows the intelligence services direct access to the comp

The term direct access was first used by the Guardian in their original story: "but the Prism program allows the intelligence services direct access to the companies' servers." - most of the early denials (where the companies presumably hadn't read the article) didn't include the phrase but the later ones did. So it's reasonable to suppose that the article was the source of that phrase.