There's two middlemen layers in this game of telephone:
1. What the leaker communicated to news outlets
2. What the news outlets communicated to us
It seems likely that exact terms and technical capabilities have been misunderstood or misinterpreted. Already, there are common misconceptions arising from the public's interpretation of the news...for example, conflating the NSA's deal with Verizon to the PRISM program. And there's also the natural confusion that generally arises in any discussion of government surveillance programs...some people seem to be surprised that the NSA is spying on foreign communications, when that is pretty much NSA's raison d'etre.
I think we should take Page as a clear denial, that is, that he's not weaseling out on a technicality. That doesn't mean he couldn't be flat out lying, of course. I think it's also a believable that if Google were to participate in a program like PRISM, that Page would be one of the people in the know.