The security impact of the relationship between RSA primes is well studied. Also: if you know q and n (which is p * q, and also public)...

It's always possible that NSA has new science unknown to the rest of the world. But they've also always been huge consumers of compute hardware, so an attempt to read tea leaves here is pretty much conspiracy-theoretic. If you believe this, there's no reason to believe any (practical, non-information-theoretically-secure) crypto is safe.

Proving a negative is awfully hard - well studied doesn't quite cut it. RSA and NSA have a history that precedes the apparent invention, so it's interesting that the tech was allowed to proceed (patents can be seized and kept secret.) I've pointed to an assumption, you've assumed a belief on my part - that's something of a conspiracy theory on your part, it's nothing I've said. The history of cryptography is replete with examples of assumptions of safety that were spectacularly overturned, and that's all I'm pointing to.