But the picture I'm getting is that they 'collect' everything (via fibre intercepts etc), because they've interpreted the rules as being "collect everything but then ask permission to look at it"
"Collect everything; analyze later" is not a feasible strategy. Nobody has that kind of storage, and even if they did, nobody has the CPUs to ingest the stream. I think it goes without saying that you need a Google-scale computer to ingest Google-scale network traffic, and that's just one of the companies in question, on top of all the public transit bandwidth. Nobody has presented any evidence that the NSA has computing facilities on that scale. The only one we know of is not yet built, and way too small.
I think it is completely feasible that the NSA would or does collect all or a great deal of voice traffic, because that's a tiny piece of network traffic these days.
I've always assumed the US gov't does have this computing power and that's why we spend so much on national defense. Besides, when you employ more mathematicians than anyone else, I'm sure you can come up with some smart ways to store big data. Also, I think it would be fairly cheap to just write everything out to tapes or disk and dump them in a closet, even if you don't have the money to load them all in a database (so that you can put them online when technology improves or you have more budget/time). Further, I haven't seen where Snowden clearly retracted his 'direct access' assertion. You might keep some identifiers in a database and the whole dataset on a user can be ingested on demand from Google or whichever company (even if that means sending an automated request to Google which automatically responds by dumping data to FTP).
Did Snowden say "direct access" in his interview or elsewhere? I thought that was an extrapolation of journalists writing about his story afterward (who also got details like the salary slightly wrong), taken from the wording on the slides, and reinforced in people's minds by the denials from Google et al which talked of backdoors etc? I don't think he made any claims about direct access, only that he could access all account details including emails etc if he had 'the proper authorities' as he puts it (which is pretty consistent with the slides and with the Google claims).
I don't remember him using that particular phrase at all at least in his initial video - I remember him talking about the ease with which they could access data using a 'selector' like an email address, not making claims about specific connections to servers or anything similar. He's not responsible for what journalists say, and we can't expect them to clearly restate it all the time, but what we do know about the extent of surveillance is disturbing. It's still unclear exactly what is recorded, when and how and I'm sure we'd all love to know more, but in the meantime it's not very useful to try to discredit his claims based on the interpretations of others.
My beef with the phrase though is that Greenwald keeps repeating it and sticks by the story that the NSA slides said it so it must mean something, without bothering to ask his supposedly very knowledgable source to expand further on the topic.
