The guess here is that the creator of this bogus document didn't have the real document at all, and thought that putting a phony certificate number on it might give the forgery away - if that number could be checked against the state birth registry.
That is an EXCELLENT point. My guess would be that real copies are made on special blank pages with pre-printed consecutive numbers. The numbers are often in red ink and are done in a funny font that the typical word processing program probably lacks.
If it's a forgery, a certificate number can't be used unless the odd font is available. So, the logical thing is to black it out that area as if protecting the individual's privacy. Which as you point out makes no sense; there is no reason to redact the certificate number.
Bingo! We have a winner. If the real number was posted, ANYONE could request a Letter of Verification from HI conforming all specific information on this document. They won't tell you info you don't know, but they will CONFIRM info you do know.
"Please confiorm that birth certificate #123456 was issued in the name of XXXXX"
"Please confiorm that birth certificate #123456 contains a race of "African"
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