The explanation that best fits the facts to my mind is that Grandma Toot tried to file something with the Hawaii DoH in August 1961.
This filing is what triggered the newspaper birth announcements.
But the birth claim that Grandma Toot filed was a half-handwritten, half-typed dodgy paper that if anyone actually looked at, would raise more questions than it answered.
So Obama’s solution was to come up with a birth certificate that looked like a normal document someone born in a hospital would have, and so hopefully questions wouldn’t be raised as to whether he was really born in Hawaii.
And of course if there is no Hawaii birth certificate for him back then I would imagine it would have been difficult for him in later years to get a social security card to get a job or perhaps even to go to college. I mean, you don't just go into a social security office and get a SSN without some proof you are an American citizen and not a tourist from Mexico or Kenya.