It's the NYT for crying out sake! Unless you believe they have the knowledge on staff to do any sort of
original reporting on this, this story is exactly what a "government official speaking on the condition of anonymity" has whispered to them. It's the fricking party line.
It's right there in the article:
The current and former government officials who described the episode spoke about it on condition of anonymity because of classification rules.
There are two options here, obviously. Someone revealed actual classified information, in which case apparently multiple government workers committed a felony to tell the NYT about a story that is entirely flattering for the employer they just betrayed. Or, and given the incidence of "government officials .. spoke on the condition of anonymity" in NYT stories the far more likely option, the press office of the NSA called the NYT, whispered some dangerous words about "off the record" and then delivered the official press release that for some reason they just didn't get to put on NSA website just yet.
This is the NYT writing a government press release into a bad thriller guided not by independently verified facts (how could you) but sheer ideology to fill in the gaps.