Your point is well taken. Courts should be able to deal with all sorts of complicated legal arguments that surround this issue.
However, I was looking at it from the point of view of the "court of public opinion". The public doesn't do well with complicated legal arguments. The arguments for ineligibility need to be simple and convincing. They aren't, and that's why this doesn't fly.
The arguments are pretty simple, until case law language is cherry-picked.
The intention of the clause in the constitution is to limit the presidency to those who have undivided loyalty, from birth, to the US. There is a risk inherent in giving the presidency to a person having dual or divided citizenship.
The prevailing legal "wisdom" is that a child born in the US, to two non-citizen parents, who is raised in a foreign country by those foreigners, is a natural born citizen. The logic is that the ONLY factor that matters is location of birth. This, they say, is what the Constitution intends by the words "natural born citizen." The allegiance and citizenship of the parents is irrelevant, according to the prevailing legal "wisdom."
It is not so complicated as you wish to make it. The Founders wanted to protect the office of President from coming under the influence of a foreigner. A child of two citizen parents is more likely to be loyal to the country, than the child of a citizen and an alien. There is the chance that the child will assume the loyalties of the non-citizen parent, as seems to be the case here. A little common sense goes a long way in understanding things that were written when common sense was still common.