The State of Hawaii only confirmed that a Certificate of Live Birth exists and is in the Vault. They did not say what was in it. This doesn't mean the information is authenticated.
Actually not even that. Dr. Chiyome Fukino spoke of "original vital records" in her second statement. (I'd never noticed the plural, 'records' before.) and "original birth certificate" in her first statement. Neither time did she use the term "Certificate of Live Birth". There are other types of documents that fit either description.