"If the government laid a subpoena to get iMessages, we can’t provide it. It’s encrypted and we don’t have a key."
There's no wiggle room there. He's not saying we don't have the users key, he's saying categorically they can't provide iMessage information. I don't understand why you think that can be read as they can't get the information through mechanism X but that they can through mechanism Y.
That's not to say the NSA can't read them - possibly with Apple's help, possibly without - but he's really not in a position to talk about what the NSA can and can't do.
From a corporate PR perspective, he really doesn't have to say anything about this. He doesn't do many interviews, he could have declined this, or declined to talk about certain topics as part of the conditions around doing the interview. If Apple can indeed read your messages then the easiest thing for him would be to shut up and say nothing so it would seem odd to go public with a lie when he has that option.