That’s only true if born abroad. If born in the US it does not matter.
Your talking about native born right?
The law, 8 USC 1401 and 8 USC 1409, which covers out of wedlock births) doesn't cover Natural Born citizenship, but that isn't even what it says for citizenship at birth. For one US parent there are restrictions as to the residency period of the parent in the US (now 5 years, 2 of which must be after the 14th birthday, but in 1961 it was 10 years, 5 after the 14th birthday, which Obama's mother did not satisfy at the time of his birth. So, if born outside the US, he's an alien, not a citizen at all) For those with two US parents, it only requires "a residence" in the US for one of the parents.
But such persons born outside the US are not even native born, they are naturalized at birth, per Supreme Court rulings, and thus are not eligible to the office of President. They don't even have 14th amendment status, since they were not born in the US, nor naturalized in the US.
Yes it does.
It's not even true then.
I am a US Citizen. I live and have always lived in the United States. My wife is Canadian. She is still residing in Canada and I visit across the border spending nearly half my time there until we can get custody issues with her daughter from a previous marriage resolved.
Our son was born in Canada. He is still a natural US citizen at birth, because I am a US citizen, and have lived as an adult in the US for far more than the required number of years. We do have to jump through some hoops to claim that Citizenship and pay a sizable fee for the paperwork, but he isn't granted citizenship by that process. He is already a US citizen, the government just hasn't properly recorded that fact yet.
A Naturalized Citizen is someone who was not born a US Citizen, but becomes one at a later date.