Man in the Middle attacks work even if one goes to the official site. It could have looked something like this.
1) User attempts to go to the official site https://...
2) NSA intercepts the message, downgrades to http and sends back a dummy site with the malicious binary [1].
3) The user doesn't notice the change and uses the malicious binary.
Today, a series of steps have been taken to make such an attack more difficult. Now browsers tend to try to warn the user and sites can take advantage of HSTS preload lists[2]. However, this article was written about an event in early 2000 when many of these safeguards didn't exist.
[1] https://en.wikipedia.org/wiki/Downgrade_attack
[2] https://blog.mozilla.org/security/2012/11/01/preloading-hsts...
Finally, it wouldn't do them any good for trying to crack things that are already encrypted with it, which from the conversation does seem like was at least one of their goals. (Could be deception, but that's the most likely reading, to me.)
I'm just saying that that doesn't seem to be a likely reason for requesting the source code.
The reason is likely what they said it was: they want to look at the source code to see if there's some way to crack the encryption faster than they otherwise could - for example, some bug causing key generation to be somewhat predictable.
The original is both pay to own and not available outside of the US. So changing either of those things would work.
You have to think that intelligence agencies have people inside hacking groups, giving backdoored hacked products a sheen of legitimacy.
But also, if they did want to do that, they could probably backdoor it pretty easily just by patching the binary a bit. Reverse engineering and changing binaries is way easier than cracking encryption, and they probably have some of the world's top reverse engineers.
The fact that they asked for an existing algorithm backdoor, among other things, makes me think they really were trying to crack at least one thing encrypted with it. As for whether it was to deal with a time-critical situation or whether that was just a confidence trick to make him more likely to give up the code, who knows.