The other possibilty was a birth aboard ship where the ship has a nursery with employees who take care of the children of passengers. Madsen Lines operated passenger ships which sailed between Hawaii and the mainland.
On the matter of the birth announcement in the Hawaii newspapers, wouldn’t the recording of a homebirth to the Department of Vital Statistics generate inclusion of the birth in the newspapers?
On another note the record at familysearch.org has bothered me so I asked a neighbor (who is a Mormon) who exactly can report a geneaology family record for the Mormon files and she informed me that anyone can. Sure makes me wonder since the Dunham/Obama link was filed by a David A. Larson. When I googled that name the majority of hits was for an architect in Chicago.
I don't think much of the shipboard birth suggestion--there isn't anything that fits with that. How does she get back to Mercer Island before she learns to change diapers? A ship coming from Hawaii to SF? Why was she doing that? She disappears from the Hawaii record around year end 1960. Sure, her family might have put her away some where but there isn't anything in the record to suggest that as distinguished from Sarah and the two half siblings who claim to have been present when he was born.
And the recent interview with Barack Sr.'s first wife--she got to be good friends and comfortable with Stanley Ann; when or more important where did that happen? In the year they were ostensibly married? The first wife was in Kenya.
First wife got to be good friends with second wife after second wife split the sheets with Barack Sr.? When? Where? And under what circumstances?
The first Hawaii newspaper claimed that what they were doing was reporting Vital Statistics obtained from Dept. of Health. That's the whole point--how you might have had a birth report in Kenya reported in the Hawaii Vital Statistics department. The homebirth fairy tale is one way. Another is a cooperative doctor.
I take it as fairly clear that something like that happened and the reason they don't release it is because it also makes it clear that the birth didn't really happen in Hawaii--or more likely, that the birth in fact occurred in Kenya.
Copies of birth records from Kenya are scattered in places around the US. A determined investigation might well turn up a copy of the true record of the birth in Kenya. The Mormons have significant expertise in this area.