It's really a shame you posted up so much verbiage only to arrive at a categorically wrong conclusion.
The issue with Obama is the *place* of his birth. He claims he was born in Hawaii, a lot of folks (myself included, as well as a bunch of Kenyans themselves) claim he was born in Kenya.
If he were born in Hawaii, even to one parent who was a US citizen, he would be "natural born," due to his being born on US soil. That's straight from English common law and its natural law foundation, and is why we consider even children of immigrants here legally who are born here to be natural born citizens.
However, if Obama was born in Kenya, then he finds himself in the exact same place that Cruz does, and is likewise not a natural born citizen.
This was the whole reason why the Wong Kim Ark case was even reference - it ruled that a child of immigrants who was born here on US soil was a natural born citizen based on the principle of jus soli.
The court ruled that Obama was a natural born citizen because it believed his argument that he was born in Hawaii.
No court ever ruled that Obama was a natural born citizen. They just refused to hear the case about it.