That is the real birth certificate.
Hawaii’s official Department of Health, Vital Records webpage: “Amended certificates of birth may be prepared and filed with the Department of Health, as provided by law, for 1) a person born in Hawaii who already has a birth certificate filed with the Department of Health or 2) a person born in a foreign country” (applies to adopted children).
B. A parent may register an in-state birth in lieu of certification by a hospital of birth under HRS 338-5.
C. Hawaiian law expressly provides for registration of out-of-state births under HRS 338-17.8. A foreign birth presumably would have been recorded by the American consular of the country of birth, and presumably that would be reflected on the Hawaiian birth certificate.
Thank you, but I have no experience with law in Hawaii. I will be looking into the law and the official records of the law soon, but today has just kept be busier than a tied up dog. Your info is encouraging.