If he wasn’t born in any Hawaiian hospital, then which hospital confirmed his birth certificate?
Thousands of babies born in the US were not delivered in hospitals, and that number is multiplied for births occurring in foreign countries, especially Kenya. However, I assume that the process for obtaining a Kenyan birth certificate for a home-birthed baby required the signatures of witnesses, especially the TBA (Traditional Birth Attendant). Why this scenario has never been mentioned is beyond me.
Until recently, the vast majority of women in Kenya have usually given birth at home. The birth of a child in Kenya is a big deal for the entire community where he or she is born. Most mothers cannot afford medical care and that's why a midwife, or "traditional birth attendant" is the one delivering the baby.
However, we are talking about Stanley Dunham, a wealthy American mother who could certainly afford to deliver Obama in a hospital (assuming, of course, that Stanley was Obama's biological mother), and while traditional home-birthed babies may never get a birth certificate from the Government, I'm sure that Obama's mama did.
Now, in order to get an out-of-country birth registered in Hawaii, an original birth certificate from the country of birth has to be surrendered to Hawaii. Regardless of whether Hawaii issued, in exchange for the original one, a long-form, Hawaiian Certificate of Live Birth (NOT called a COLB), or a Hawaiian Certification of Live Birth (what IS called a COLB), the name of the actual country of birth would be listed under CITY, TOWN, OR LOCATION OF BIRTH on either form. Of course, the ISLAND OF BIRTH on the COLB would be left blank, or would say "NONE."
Since both documents may list only the location where the birth occurred, that means the name of the ship if a baby was delivered at sea, or the closest intersection to the location of the taxi if the baby was born in its back seat.