Whether Barry himself was a British national at birth under British law, is of no import. The citizenship status of his father at the time of his birth is what counts, at least under the Vattel "Law of Nations" definition of "Natural Born Citizen".
The natives, or natural-born citizens, are those born in the country, of parents who are citizens.
BHO Sr was not a US Citizen, so BHO Jr cannot be a Natural Born US Citizen. (That quote is from the 1852 translation by Chitty, however. The original French said "The natives, or natural-born citizens, are those born in the country, of parents who are citizens." The original French said "naturels, ou indigènes" apparently the translator turned the order of terms around. The earlier, British, translation said "natives, or indigenes". The founders would have read the original French version anyway.
I agree with you, but the reason the nationality of the father is important is that it devolves upon the son. If Obama SR. WERE NOT married to Ann Dunham, he would not have passed on his nationality to his son, and most likely as a child of a single unmarried US citizen mother, only her citizenship would have been taken into account. There would not even have been any requirement for Ann Dunham to name the father on the Birth Certificate.
All of this assuming, of course, a Hawaii birth location.