I don't know that anyone would swear that the information is accurate, but rather than it reflects the information on the original Certificate, which might have been fraudulently submitted. This would be easy to do, if one claimed a "home birth". In '61 the child would not have needed to be physically present in Hawaii for that to happen.
Yes, I would think that's right. It would be impossible to swear that the information was "accurate" without having some first hand information of the birth itself. They would be attesting that the form was completed commensurate with the information that the state's information systems had on file, which presumably mirrors what the original had or has.
Would that be enough? I don't know.