I can’t see how the naturalization process could have ocurred. He must have used a US birth certificate to gain his passport.
Looking at http://travel.state.gov/passport/get/first/first_4315.html
it looks like he could have gotten a US passport by showing a Kenyan birth certificate and proof of his mother’s citizenship. But that would have required a statement from his mother so it would have had to be done before she died.
A delayed birth certificate (such as the one Obama achieved in 2006) would work for a passport, with no other documents, if the BC lists that an affidavit by the parent is on file. That situation means that you can get a US passport merely on the word of the parents, whereas Hawaii seems to require incomplete medical information to be supplied by a doctor.
His Grandma could have signed a birth affidavit anywhere along the line, but there would have had to be “early records” as well - one of which is a baptism record (although it doesn’t meet the PREFERENCE that it be created within the first 5 years of life).
I’m sure Jeremiah Wright would have been happy to say on Obama’s baptism certificate that Obama was born in Hawaii. That’s one of the documents which has never been allowed to be made public. I know at our church we issue baptismal certificates but don’t keep copies; however the information for the baptism is recorded in the official record books. There was a time in MN when the church’s baptismal record from the official record book was used to get a birth certificate.
So there are ways it could be done even since 9-11. I wonder how the rules governing passport documentation have changed over the years - specifically whether 9-11 changed anything. To be in the US Congress a person has to be a US citizen - although that means nothing if nobody is allowed to check the documentation.