To the best of my knowledge no one ever made the argument that you are making and Hawaii law allows a confidential birth record to be released for inspection under court order from a judge of a court of competent jurisdiction.
Hawaiian law allows all records to be released to the public in good faith to meet the public interest under its sunshine laws. Of course, the law doesn’t require the records to be released, but they are still allowed to be released. Hawaii simply refuses. But the other point here is that under their own state laws, if such a record is not given to the opposing party for inspection then that record is considered hearsay and is inadmissable. And this is where we are at legally. Obama’s alleged birth in Hawaii is hearsay. It has never been legally certified.