From the US State Department website:
Birth Abroad to One Citizen and One Alien Parent in Wedlock: A child born abroad to one U.S. citizen parent and one alien parent acquires U.S. citizenship at birth under Section 301(g) INA provided the citizen parent was physically present in the U.S. for the time period required by the law applicable at the time of the child's birth. (For birth on or after November 14, 1986, a period of five years physical presence, two after the age of fourteen is required. For birth between December 24, 1952 and November 13, 1986, a period of ten years, five after the age of fourteen are required for physical presence in the U.S. to transmit U.S. citizenship to the child.
But of course that's for children born in Wedlock. If he was born outside the US and out of wedlock then the following applies
Birth Abroad Out-of-Wedlock to a U.S. Citizen Mother: A child born abroad out-of-wedlock to a U.S. citizen mother may acquire U.S. citizenship under Section 301(g) INA, as made applicable by Section 309(c) INA if the mother was a U.S. citizen at the time of the child's birth, and if the mother had previously been physically present in the United States or one of its outlying possessions for a continuous period of one year.
But notice "may acquire", meaning not a citizen by birth or a natural born citizen?
Go to page 2 and you will see the law that fits Obama's circumstances since he was supposedly born in 1961.
"4. December 24, 1952 to November 13, 1986
If, at the time of your birth, both your parents were U.S. citizens and at least one had a prior residence in the United States, you automatically acquired U.S. citizenship with no conditions for retaining it."
"If only one parent was a U.S. citizen at the time of your birth, that parent must have resided in the United States for at least ten years, at least five of which had to be after the age of 16. There are no conditions placed on retaining this type of citizenship. If your one U.S. citizen parent is your father and you were born outside of marriage, the same rules apply if your father legally legitimated you before your 21st birthday and you were unmarried at the time. If legitimation occurred after November 14, 1986, your father must have established paternity prior to your 18th birthday, either by acknowledgment or by court order, and must have stated in writing that he would support you financially until your 18th birthday."
The law you are quoting is the 1986 law. It is not retroactive except for Military families.
Follow Davids postings on this. He states he is a lawyer and has given a good explanation of it. In fact David may give you the link to his explanation.