Congress has arguably had no meaningful oversight over the NSA since the 50s. Eisenhower warned us. He wasn't just talking about defense contractors. One might say that the US has been pwned by military hackers. I highly recommend Bamford's books.

Congress has whatever oversight it wants. They can simply defund any agency that irritates them.

The NSA, the NRO, and the NGA are DoD agencies. The DNI -despite the title- has next-to-nothing to do with running those agencies.

To analogize: The US Army answers to the DoD. The DoD answers to the POTUS. This the Army and the DoD are military organizations, despite this fact.

Yeah, I understand that. I only included the DNI because he did.

No. You included the DNI-is-part-of-DHS factoid because you thought that it bolstered your claim that "The NSA is not a military organization.". [0] You were wrong. :)

[0] https://news.ycombinator.com/item?id=9598793