This is the heart of your question.
I think that the information we have is such that there are two possible opinions on this topic.
The first is that our president's father may not have been legally married to our president's mother (as he had an earlier wife in Kenya). If that is the case would a single mother giving birth in the USA to a child not have that child be “naturally born?” Remember your argument seems to hinge on our president being born in a way that he had dual citizenship. If there are dual citizenship records for him, then yes, he is not a natural born citizen. If there aren't then he might be argue that his father's marriage to his mother was not legal and so he was a full US citizen at birth by an American mother within the USA.
Second, the question is what is a natural born citizen. We know what the Original Constitutional provision states and if there was a legal marriage and he had dual citizenship, then yes, I think perhaps he should not be eligible to be President under the Constitution as it was written long ago. But there have been amendments and there have been interpretations by the courts of citizenship and some of them use the terms natural born citizen. Under some of those changes that I have read, one could make a compelling argument that our president is eligible to be in the White House (as despicable and incapable as he may be).
I think folks would spend better time checking out his early school records to see if he claimed to be a foreign national, if he had a non-US passport, and why he seems to have had multiple social security numbers.
As to natural born, I will leave that one along, as I between what has been produced (which I believe was doctored) and the INS report on his father that says he had a child in Hawaii, are pretty compelling (although I do want to read the new book out to find out what has been found by that Harvard graduate in his research.)
Call me a rule of law (as amended and interpreted by the courts) kind of guy.
What is a natural born citizen.
This is the heart of your question.
To some, yes. However there is another valid question, and that is “what does the document released this week prove?”
In my opinion - the answer is “Nothing”.
It is a pdf electronic document, which is composed of various graphic elements. Anyone who knows how pdfs work can verify this. What is NOT is an image (like a scan or photograph) of a piece of paper.
Maybe years ago there was an original Obama HI birth certificate that was ultimately the source of the information that was contained in the pdf. If this could be proven I’ll be the first to agree this document carries some weight.
But without that proof - the textual content could as well have been typed by any of us.
Once you understand what the document is - and isn’t - the value of it as proof of birth disappears. All the original questions are still open, along with new ones, such as who created this pdf form, when, and why?
His mother was NOT 18 when he was born, so couldn’t confer citizenship on him. So even if his mother wasn’t legally married, he still couldn’t be a citizen