If "Osama" Obama were born abroad, he would not be a natural born citizen, because his father was not a citizen although his mother was.
Actually, not only because McCain had TWO American parents, but it helps. If a baby is born abroad to ONE American parent and one foreign national, but the American parent fulfills the requirement of a certain number of consecutive years in the USA as an adult, the baby is “born an American” and thus natural born. My son is one of these.
In your Barack Obama example, apparently his mother could not have been 5 years in the USA as an adult (or over the age of 15?) because she had him at 18 or 19. So his birth records really do become significant to determine his eligibility.