Spooky - it's spooky how you're getting ETOPS, NATS, and Hawaii qualification all mixed up.
Of course the training program is FAA approved. Who said it wasn't?
Could you find the section of the AC you refered to that requires a simulator session and two ETOPS legs with a CKA before you can fly to Hawaii and post it?
I just checked our ops spec and it doesn't exist. I also asked a CKA if a Hawaii ETOPS checkout was required. The answer he gave was no. But rather than just rely on his word I checked our FAA manual. The CKA was right, there are many ways to get the requirement waived.