The state of Hawaii says he was born in Hawaii. That is good enough for me as well as any court and any Federal agency. Why does it not satisfy you?
Technically you are quite right because the COLB appears to be sufficient for a court of law. First of all the back of the certificate is stamped with the statement and signature of Dr Alvin T. Onaka PhD. It has been stated the Doctor signed so many certificates he had hand problems. Thus the rubber stamp is the verification used. A rubber stamp would not stand up too well in any court, if challenged. Anyone could pick up a rubber stamp and wield it.
Unfortunately the State of Hawaii appears to have been in a few instances only too kind to issue a COLB. This on the statement in good faith by a person who claimed their offspring was born there. There is the case of Dr Sun Yat-Sen (1866-1925). He had a birth certificate on his statement he was born in Hawaii. He was not born there. I would presume if his enemies were out to kill him, he could avail himself of the US embassy in China. Clever stuff.
The long form, if it exists, awaits posterity, genealogy buffs and last but not least - American public.
Actually, his aim was to travel to the mainland in violation of the Chinese Exclusion Act for the purpose of fund raising to help the Chinese Revolution. Of course, if he had known Mao would come along, maybe he'd have cooled it.
BTW, Obama and Sun Yat Sen attended the same high school.