Personally I expect that a president has the same rights as we do; i.e., it's available only if s/he says OK. Of course, if s/he refuses to release it then we have another Obama.
Even if Obama releases his long form B.C. -- as all of us have been required to do from time to time -- that still may not end the arguments.
For example, my long form B.C. is stamped Delayed. I was not born in a hospital.
I could have been born anywhere.. or simply found somewhere.
I believe that all that's required to register is a doctor's signature that the baby is in good health and signatures of one or more(?) witnesses to the birth, depending upon state law.
You may not have been born in a hospital but is there a provision for “midwife” on your form?
There is on mine and many other I have seen including the one for my friend who is 99.