Because at least one head nurse/administrator is likely a deputy registrar authorized by the state, much as a notary or a title clerk. And that nurse probably wouldn't assign the certificate number. She'd just sign the form and datestamp it once she verified all of the proper information was filled out.
Even butterdezillion acknowledges that a hospital employee was likely authorized as a local registrar.
You’re still full of suppositions. It’s better than likely that the Obama COLBs that were published online by the DailyKook.org and the nonfact checkers at “Factcheck”.org are forgeries.