You are painfully obtuse, aren't you.
Obama enjoys the same HIPAA protections about his birth certificate and any other piece of individually identifiable information any hospital has on him, including any HI hospital. As such, his hospital of birth is not allowed to make any comments about his birth, or provide any documentation about his birth, including his birth certificate. I'm not familiar enough with HI law to know if the hospital can confirm, deny or make any comment about a birth - there may be a safe-harbor provision that allows a HI hospital to confirm a birth while the newborn is an active patient at the hospital.
The state of HI is NOT an open records state with respect to vital records. In fact, they're about as closed as you can get for vital records. Like many states, only individuals who are the next-of-kin for a subject (in limited circumstances) may obtain copies of Hawaiian birth certificates.
We have one object - a birth certificate - that is controlled by two different sets of laws and in two different circumstances - HI state law controls how the BC is managed in state custody, and the federal HIPAA law controls how the hospital copy of the birth certificate is controlled.