The father was known. Sorry, your theory of paternal influence being nugatory shot down in flames.
Only when the father is UNKNOWN does the law of ‘natural born citizen’ work only through the mother.
Are you just making up stuff up as you go along?, the Immigration Code doesn’t distinguish between Known or Unknown Father, but instead looks at the mother’s marital status. Since as you pointed out Obama’s father was already married to someone else, so the President’s birth as out of wedlock.
7 FAM 1133.4-3 Birth Out of Wedlock to American Mother (TL:CON-68; 04-01-1998) a. Section 309 (c) INA: A child born abroad out of wedlock after December 24, 1952, to a U.S. citizen mother acquires U.S. citizenship if the mother was physically present continuously for 1 year in the United States or its outlying possessions at any time prior to the child’s birth.
gotta examine BC for this.