That's reverse psychology. They know everyone will lose trust in Rust and go back to memory unsafe languages so they can hack our software again.

• put my tin foil hat aside -

You might want to have a relook at your own statement here. It's got a load of paranoia. Paranoia beyond common sense and realistic threat assessment is unhealthy.

As for the NSA, it's like they have a split personality (which I think is true for anyone in their position). Their job isn't all about stealing information. They also have the mandate to secure their own and their allies' assets. After all, who knows what's more vulnerable to thievery than an experienced thief? Their job is as much to harden security as it is to compromise.

Finally, their statement is to move to a safe language - one of which is Rust. For your apprehensions about their backdoors to be true, they'd have to compromise every memory safe language out there - Rust, Go, Swift, Nim.... There's reason to be suspicious if they recommend only one language (that is more or less what happened with the NIST pseudorandom generator algorithm). But that isn't the case here.

And you need to assess statements on their own merit - not based on who says it. What they say is true even in our personal experiences. It's been shown statistically that people write much fewer bugs (memory safety bugs are a huge class) with safe languages. I'm not even confident of writing correct C programs these days. Honestly, if your paranoia is true, then it's easier for the NSA to recommend everyone to write in C or C++. That way people will write careless mistakes that they can exploit. And C/C++ usage is way more than for Rust or anything else. They'd target C/C++ compilers and standards to increase their impact.