As a matter of fact, there is dictum here in which this Court approves earlier dictum in Steinkauler that a person who becomes a citizen by right of birth in the US is eligible to run for president (Natural Born) even though his father was not a citizen.
Parental citizenship has ceased to be an issue because of the 14th Amedmdent.
And in fact, as I have pointed out, under current law in many of the Euro countries, where a grandfather who immigrates to the US and has a son born in the US who in turn has his own son born in the US; both the first generation son as well as the second generation grandson are both citizens of the Grandfather's country of birth (as well as "natural born" citizens of the US), even though they may not be aware of the fact.
None of this has been of great concern with respect to the Obama situation--at this point, everyone in the knowledgeable political establishment, as well as those of us who have studied the issue here know that Obama was born in the Coast Provincial General Hospital, in Mombasa, in what is now modern Kenya.
Steinkauler's father, was a Citizen at the time of his birth. So was Elg's. Both were naturalized, but they were citizens.