They do typically eat their own dogfood when it comes to the security practices they propose. Dual_EC_DRBG is the big exception, but it's generally considered that most of the rest of their cryptographic standards are secure and suitable for public and government use.

There are likely many conflicting departments and teams within NSA. Many are probably trying to fight for the public's security and have for years, with cryptographers earnestly trying to develop secure and efficient algorithms. They are probably at odds with the other forces in the organization that seek to play the espionage game, even if it puts the country at risk.