Earlier quoted context omitted.
Hm, what’s wrong with just calling? It is probably the easiest way to find out whether someone is generally willing to cooperate, and if they don’t, the NSA doesn’t lose much either?
NSA was long nicknamed "No Such Agency" for a reason - they were, and to an extent still are, notoriously secretive compared to other US intelligence agencies. I'd expect them to approach it via intermediaries. Frankly it sounds more likely to me that this was a poor attempt at social engineering rather than a genuine contact from the NSA.
Seems like you could really play this NSA stuff up in social engineering attack, especially if you were willing to put some work into it. Imagine grabbbing the NSA logo off their website, and make some fancy looking, seemingly authentic laminated plastic ID cards, then show up at someone's office asking for data/access/etc. and claiming to be from the NSA. Even hand then a "National Security Letter" and carefully explain the gag order to them, and let them know that doing so much as picking up the phone to call anybody else to ask about cooperating could result in them being jailed. Subtly hint that "jailed" might mean "disappeared to Guantanamo".
Since everybody knows that the NSA is kinda "in the shadows" and lots of people have heard of NSL's and gag orders by now, I imagine you could get a lot of people to go along with this. Especially if you had two big, physically imposing guys in nice suits to play the roles.
(edit: I am, in this case, mainly talking about inside the USA, where NSL's have authority, etc.)