Since I’ve never even visited Hawaii take this response for what it’s worth! My experience in New Mexico was the polar opposite of what you outlined. I registered with a State site and received a notification appointments were available and how to schedule. Once scheduled I arrived at the location and literally walked in and gave them my name and Date of Birth, sat down and they injkected my vaccine. They also gave me the card showing brand and date of injection. At the time I was waiting, 15 minutes in my case, I received my appointment for the second injection. At no point was I asked about insurance. I’m not so naïve that there is enough information traded around that “they” could not have found my insurance and/or Medicare information if they chose to.
As I understand it the Federal Government is paying for the Vaccine however this link indicates this:
Vaccine providers can be reimbursed for vaccine administration fees by patients’ public or private insurance companies, or by the Health Resources and Services Administration’s Provider Relief Fund for uninsured patients.
So it’s somewhat sad that the folks in Hawaii are inclined to put people through hoops just to receive the vaccine. Good Luck.