If Bill Binney said that, and if he is right, I'd assume the most likely explanation is that NSA can push over some low-security SSL connections of the type jerf describes above https://news.ycombinator.com/item?id=5877362 , but has to rely on "direct access" to get around most or all high-quality (but still widely-used) SSL encryption. (Or, again, that it also has the capacity to break high-grade HTTPS connections, but it's holding that back for really important occasions.)
With the history of the gov/NSA being effective crypto gods - my money is they are ahead of decrypting SSL and HTTPS and even of it is not real-time, they store streams from target end points regularly for slower offline decrypt.
I wonder why so many people believe this. Many simple and weak ciphers have been around for decades and - although they are considered to be very insecure by cryptographers - certainly can't be decrypted in real-time (!) on this scale (!).
This has been talked about many times now. All compromising a CA lets them do is to create believable certificates to be able to man in the middle connections, but they can't be doing that for a large number of connections because it's resource intensive and detectable.
They still don't have the private keys of the sites if they break into the CA.
I find this quite plausible, with or without the knowledge of Page, Zuckerberg et al. the NSA might very well have the private keys of these companies. I would not be surprised if the CEO's of these companies choose to be ignorant of the NSA's methods to not have to lie to the public, shareholds and Congress.
Also, given that the world's best engineers work at either high-tech companies or the NSA there will be some who have switched between these industries, giving the NSA/CIA a headstart to get any information these companies hold through old-fashioned spy-tactics.
