So you are saying this is us?
I am not sure I all the way understand.

I am a simple fellow.
Who gets called when I fill out the 4473?
Is the FFL not doing a background check?
If my permit is defacto a background check, why do I have to do a 4473?
In most states, the NICS background check is instant (it's in the name). For most sales, the FFL submits the 4473 info via Internet, The FBI looks up your records in several database, and they approve the transfer in minutes.
If the FBI has problems or questions concerning your applications/4473, the FBI has 3 days to adjudicate it. If they don't reject you in 3 days, the transfer is automatically allowed.
For Hawaii NICS, the only differences are:
1. The FFL submits the 4473 to HPD for approval -- not to the FBI.
2. The process takes 2 weeks if you have to apply for a permit. it's "instant" if you already have a long gun permit and if that's what you're buying.
3. NICS results go to HPD, not the FFL.
All interaction with the FBI is through HPD. HPD is the "POC" (Point of Contact) for NICS in Honolulu.
Form 4473:
Federal law requires all firearm transfers through FFLs be recorded on the 4473. Dealers must keep those forms for 20 years. If they go out of business, they are supposed to send their files to the ATF for storage.