That's not how reporting works. Most likely The Intercept contacted the NSA to corroborate details, and the NSA likely figured out who leaked the document based on their own investigation. The NSA does not fuck around with internal documents since Snowden.
The Snowden and Manning leaks made the NSA revamp their entire contractor network infrastructure. Before those leaks, the NSA and State had very wide open networks for their contractors. Any contractor/grunt with a security clearance could open up a variety of files, documents, etc.
Following 9/11, the NSA and most of the IC wanted to ensure that counter terrorism investigators could access any and all information and documents at anytime. Part of 9/11 was blamed on the lack of intelligence sharing, even between different floors in the CIA, so the IC thought it would be best to allow anyone to access anything to prevent the next attack, unfortunately for them, it seems they left themselves open to leakers like Snowden and Manning.
Since then, both have made it a point to extremely compartmentalize anything and everything. The NSA knows what a contractor saw and can figure out quickly if a worker abused their power (like spying on an ex) or leaked documents.
The Intercept did not burn a source, they did their job by confirming certain aspects of the document with the NSA. The NSA likely figured out who leaked that document based on their new information sharing procedures and infrastructure with contractors.
To be honest, I wouldn't be surprised that the NSA knew who leaked the documents before The Intercept contacted them. Based on reporting by the Times and NPR over the last few years, it's clear that the NSA in particular is very proactive in investigating any and all suspicious activity committed by their own agents or contractors.
