You're confusing "Certificate of Live Birth" and a "Certification of Live Birth". A VERY common mistake here at FR. The phrase "Certificate of Live Birth" is a phrase that the Centers for Disease control uses on a document that it provided to all the states. That document, although not binding, was to be used by the states when designing their own proprietary (for lack of a better word) "birth certificate" Almost all states today use an EXACT copy of the CDC's "Certificate of Live Birth" - sometimes called a "birth certificate" or a "vault copy birth certificate" or a "long form birth certificate".
A link for the CDC form is below. You need Adobe Acrobat Reader to view the document.
http://www.cdc.gov/nchs/data/dvs/birth11-03final-ACC.pdf
The "Certification of Live Birth" is what has been bandied around by various websites, including Obama's own campaign website. It is a computer generated document that uses information that is stored in a state's database to fill out, automatically an "official" copy of a resident's birth certificate.
It is true that every court in America be it, City, County, State or Federal will use the "Certification of Live Birth" as a prima fascia evidence of citizenship. But, it certainly leaves out information that might be critical in determining a Presidential Candidate's eligibility for office.
You are the very first person I’ve ever heard addressing something that seems so simple a nuance.
Thank you.