It resulted in one of the stranger episodes in the history of digital-age journalism. On Saturday 20 July, in a deserted basement of the Guardian's King's Cross offices, a senior editor and a Guardian computer expert used angle grinders and other tools to pulverise the hard drives and memory chips on which the encrypted files had been stored.
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Twelve days after the destruction of the files the Guardian reported on US funding of GCHQ eavesdropping operations and published a portrait of working life in the British agency's huge "doughnut" building in Cheltenham. Guardian US, based and edited in New York, has also continued to report on evidence of NSA co-operation with US telecommunications corporations to maximise the collection of data on internet and phone users around the world.
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Rusbridger took the decision that if the government was determined to stop UK-based reporting on the Snowden files, the best option was destroy the London copy and to continue to edit and report from America and Brazil. Journalists in America are protected by the first amendment, guaranteeing free speech.
http://www.theguardian.com/world/2013/aug/20/nsa-snowden-files-drives-destroyed-london
And the Guardian's editor had this in mind from before - during the Wikileaks article work, he knew the New York Times had 1st Amendment protection he didn't in London:
During one of these meetings I asked directly whether the government would move to close down the Guardian's reporting through a legal route by going to court to force the surrender of the material on which we were working. The official confirmed that, in the absence of handover or destruction, this was indeed the government's intention. Prior restraint, near impossible in the US, was now explicitly and imminently on the table in the UK. But my experience over WikiLeaks the thumb drive and the first amendment had already prepared me for this moment. I explained to the man from Whitehall about the nature of international collaborations and the way in which, these days, media organisations could take advantage of the most permissive legal environments. Bluntly, we did not have to do our reporting from London. Already most of the NSA stories were being reported and edited out of New York. And had it occurred to him that Greenwald lived in Brazil?
http://www.theguardian.com/commentisfree/2013/aug/19/david-miranda-schedule7-danger-reporters
So this idea of a 'secret courier' carrying stuff into the US is almost certainly rubbish, especially done by the NYT. The Guardian took its copies in around the time the story first broke - probably before, either physically or electronically (after all, its journalists would be targets after that, and they wouldn't want to lose their only copy).