The Congress has granted the Secretary of State, and by implication the Department of State, the authority to issue Passports under US Code, Title 22, Chapter 4.. The granting of authority to the Department of State to issue a Passport implies that the authority to prescribe the manner in which citizenship must be proved has also been granted.

When this authority has been granted to a federal Department or Agency, the rules that the Department or Agency will use are then promulgated as regulations. These regulations are maintained as part of the Code of Federal Regulations (CFR).
The Department of State has issued regulations under CFR22.51.42 that state the following requirements for a citizen to prove birth in the United States:

(a) Primary evidence of birth in the United States. A person born in the United States generally must submit a birth certificate. The birth certificate must show the full name of the applicant, the applicant’s place and date of birth, the full name of the parent(s), and must be signed by the official custodian of birth records, bear the seal of the issuing office, and show a filing date within one year of the date of birth.
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Under this CFR, a Birth Certificate will be accepted as proper evidence of Jus soli citizenship if it shows the full name of the applicant, the applicants place and date of birth, and the full name of the parent(s). The certificate must be signed by the official custodian of the birth records for that state, and the record must bear the seal of the issuing officer. In addition, the filing date shown on the certificate must be within one year of the date of birth. If all of these requirements are met, the certificate is proven under the CFR and by implication, under the general laws enacted by Congress. In order for that CFR to be over-ridden, wither the CFR would need to be changed, or the Congress would have to specifically change the requirements by legislation.

The State of Hawaii has issued a Birth Certificate that meets all of the requirements of CFR 22.51.42. That Birth Certificate is certified by the State of Hawaii, and is considered proven by the Laws of the United States. It will be up to anyone who challenges its authenticity to prove, by a preponderance of the evidence, that the Birth Certificate is actually invalid.