[Non-Sequitur]

The parent’s citizenship isn’t on the certificate, but a lot of other stuff is...

You are aware that your link is to a Certificate of Live Birth and not a long form Birth Certificate, right?

[Red Dog #1]

Regardless of the document's title, this an example of a “long form” certificate from the era Obama was born.

Images of both "long" and "short" Hawaiian certificates...

http://www.google.com/images?um=1&hl=en&rlz=1R2GGLL_enDE389&tbs=isch%3A1&sa=1&q=hawaiian+certificate+of+live+birth&aq=f&aqi=&aql=&oq=&gs_rfai=