I totally agree that these organizations used the phrase "direct access" intentionally, surely with legal advice. My point, however, was that at the time that these companies released their responses, the slide that actually said direct access verbatim had not yet leaked. Although it's impossible to tell what actually happened, it looks to me like they decided to deny "direct access" in the hopes that there were no slides indicating that direct access did exist. After all, it's unlikely that these companies had the full slide deck (or anything other than what the media had published).

So, either:

(A) Larry Page and Mark Zuckerberg actually didn't know that they provided "direct" access to data.

(B) NSA actually doesn't have "direct" access as indicated by this slide, meaning that the slide is incorrect or falsified.

(C) Page and Zuckerberg lied in their statements.

I don't see a fourth option regarding direct NSA access to these companies' data.

And you're right regarding Mayer not addressing the claim directly; I was a little bit off there. Still, by saying "well, we received between 12,000 and 13,000 FISA requests," Yahoo! is implying that there isn't any sort of "backdoor" access, which no longer seems to be the case.