You're mincing words. Your comments clearly indicate that you think "direct access" unambiguously means "access to servers that run GMail that the NSA can snoop on any time they like." But from what I've seen, most comments on HN adopt and acknowledge a more ambiguous definition.
The one you propose is the extreme. But other definitions include an interface for the NSA to request data and have it deposited in some "drop box" that can then be accessed by the NSA (all without a warrant). It's reasonable to call this "direct access", particularly if the audience is not tech savvy. (Which is something we don't know.)
Moreover, most folks here seem painfully aware that "direct access" really hasn't been qualified. It seems reasonable your definition isn't really true, but that doesn't mean the Guardian's reporting is incorrect. (The Guardian never put forward a precise definition---either because they didn't have one or were unwilling to release it.)
Personally, I think you are attributing way too much certainty to the HN crowd.