Mine, my wife's, and my kids' birth certificates all recite birthplace of the parents and birthplace of the baby. From memory, none of the five certificates recite citizenship, for baby, mom, or dad.
The Nordyke twins of Hawaii, born within days of Obama, have produced their birth certificates, but I don't recall what all is on those.
My point exactly. I have yet to see anyone provide an example of an American birth certificate that lists citizenship of parents (or religion, for that matter. Another oft-cited conspiracy).
Furthermore, parental birthplace is only as volunteered by the parents. For my son's Californian birth certificate, I truthfully listed Colorado as my birthplace and my wife, his mother, truthfully listed Ukraine. We weren't required to provide any documentation to verify our birthplaces and my wife's citizenship was not inquired about. My wife could have just as easily listed "Kansas" as her birthplace and no one would've questioned it and this would've appeared on my son's BC.