They may be a National and a Citizen but they are not Natural Born Citizens, that includes Illegal Alien children.
The very first line says there is not even a way to confer citizenship to a child of an illegal alien “(a) a person born in the United States, and subject to the jurisdiction thereof;”
The parent is a citizen of another country and under that country's Jurisdiction. That makes the baby a citizen of the country their parents are citizens of.
In Barrack’s case, his father was a citizen of Kenya and that makes Barry's citizenship status a divided birth.
You can only be NBC if both parents are citizens of the US and subject to the jurisdiction of the US.
An example of jurisdiction would be the parents take a trip to Cuba. That is against federal law and prohibited to American Citizens, Natural or not.
If, however, the parents are from France, they are perfectly free to travel to Cuba with no fear of prosecution, as they are under the jurisdiction of France as citizens of said country. France has no prohibition against travel to Cuba but, if they did, the parents could only be charged under French laws for whatever crime they committed.
That is why people who commit crimes, in the USA, that will likely result in a prosecution under our laws, seek countries that have no extradition treaty or have strict guidelines for extradition.
The criminal of this country would not and could not be charged with a crime that was not committed in violation of the laws of another country.