Why is the NAUI part important?

There are several agencies that have very good Nitrox training, and
frankly, it's not rocket science.

Your best bet is to find an instructor with a good reputation, and take
whatever certification course that instructor offers. That's how I
wound up with TDI - not because I cared either way about TDI, but
because one of the best instructors I know of, Phil Sammet, teaches that
particular class.

Agency is nothing compared to instructor.

-Karl