Incorrect.
There is a difference in law between the legal father and the biological father. In most states (all I believe), and I suspect under federal law where it might be relevant, the law is concerned only with the legal father. Whether the actual sperm donor might be someone else is not relevant to legal standing.
If she was married to Pop Obama at the time of the birth, Pop is the legal father. Who the actual biological father may be, assuming it's someone else, is just not relevant.
I find the rather odd parallel to our Lord and Savior amusing. Christians believe Jesus was not the biological son of Joseph, but that he nevertheless inherited the legal right to the throne of Judah from him as the legal father.
There is a divorce document to support reversing the adoption of Obozo by Lolo Serotoro, but no document to support the marriage between Stanley Ann and BHO, Sr. At the time Stanley Ann was said to have married BHO, Sr. he was already married in Kenya. And there is no evidence that BHO, Sr. ever lived with Stanley Ann in HI (or anywhere in the U.S.). So if there is no father listed on the original BC what does that make him? If he was born in the U.S. that is one thing, but if he was born say in Canada it is quite another.
If he was foreign born and his father was not a U.S. Citizen he would not even be a citizen at all. The Immigration Act of 1952 was the law that controlled eligibility of mixed (nationality) marriage births, not the current law.