The passport lists his birthplace. Given that his parents weren't diplomats or invaders, that is sufficient to prove his natural born status that is not on his passport.
Where is his long-form B/C?
Why do you care? There is no additional information on his long-form BC necessary to prove his natural born status.
No, there’s just the kind of information that would indicate whether Obama’s birth was filed honestly and originally listed Hawaii as the birthplace.
This means that this passport merely documents an assertion of Obama's birthplace.
Proof of place-of-birth comes from a long-form birth certificate.
This isn't very difficult.