IT is a little more complex than that - they need to also figure out what codes the US government uses for classified secrets that we don't won't other countries to find. It is not clear how they resolve the inherent conflict in these goals.
For these ciphers, it seems less likely that NSA has a backdoor that no-one else could find.
Notably in the case of dual-EC there was a recommended curve chosen by the NSA. That was easy to backdoor by knowing how the curve was generated.
More importantly, pretty much the whole point of a PKRNG is to make the random state recoverable. It's not as if competing RNGs have designs that enable the kind of backdoor Dual EC does. That's what was so weird about it, and why there was some doubt about what it was --- not doubt that people should use Dual EC (of course they shouldn't, and it's been amazing to see companies like RSA and Juniper actually adopt it; the cryptographic incompetence behind those decisions was shocking), but that NSA could really be using such blatantly awful tradecraft.
