First of all, that image of the alleged Obama COLB that was put up on the internet has been proven to be fake, so NO, Obama didn't "fill out a form" to obtain it.
Secondly, the short form bc (COLB) isn't accepted as proof positive of identification by many gov't agencies, and even private institutions. Americans who were born in Hawaii still have to produce their long form birth certs, just like any other Americans. There still must be a mechanism for them to obtain a copy of their long form birth certificate, or they're in a world of hurt.
I was without a valid Texas driver's license for a couple of months, some years back, because the state of Texas accepts ONLY a long form bc as proof of identity.
Now, what if I'd been born in Hawaii, and my long form had gone missing? I'd be screwed, if Hawaii would only give me a COLB.
Also until I believe august 2009 long forms were NEEDED by Hawaiians for their special applications for Hawaii Homelands. HDOH changed that without notice in what can only be described as a suspicious activity as a front to pretend long forms were no longer available. I am concerned maybe now they have put a forgery in place after Abercrumbs slip up...