§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.
(c) The fee for each application for registration shall be established by rule adopted pursuant to chapter 91.
[L 1982, c 182, §1]http://www.capitol.hawaii.gov/hrscurrent/Vol06_Ch0321-0344/HRS0338/HRS_0338-0017_0008.htm
Yes, you are correct, I was wrong. However, the law that you cite did not exist until 1982.
And as I understand it, BHO was born in 1961 but if here were born sometime after 1982, his mom could have registered his birth in the State of Hawaii. Well, then again, you could be on to something! If Obama was born after 1982 he would not be qualified to be President.