Not true.
The Certificate of Hawaiian Birth program was established in 1911, during the territorial era, to register a person born in Hawaii who was one year old or older and whose birth had not been previously registered in Hawaii. The Certificate of Hawaiian Birth Program was terminated in 1972, during the statehood era.
Absolutely true
[§338-17.8] Certificates for children born out of State.
(a) Upon application of an adult or the legal parents of a minor child, the director of health shall issue a birth certificate for such adult or minor, provided that proof has been submitted to the director of health that the legal parents of such individual while living without the Territory or State of Hawaii had declared the Territory or State of Hawaii as their legal residence for at least one year immediately preceding the birth or adoption of such child.
(b) Proof of legal residency shall be submitted to the director of health in any manner that the director shall deem appropriate. The director of health may also adopt any rules pursuant to chapter 91 that he or she may deem necessary or proper to prevent fraudulent applications for birth certificates and to require any further information or proof of events necessary for completion of a birth certificate.