“It’s just that simple”
Actually, no, it isn’t.
Stanley Ann Dunham couldn’t have been married to Barack H. Obama when she gave birth to Barry S. Dunham, because BHO was married to Kezia already.
In 1961, illegitimate children did not have fathers - not legal fathers anyway. On this, the common law, the 1948 British Nationality Act and the 1952 US naturalization law all agree.
So, unless you have a theory of how Barry could have been Obama’s legitimate son, he did not have dual citizenship at birth.
And who do you think the real father was? If it was FMD he was an American. Hell, it could have been anyone!