You have not read the article which addresses these issues. The article discusses the differences between natural-born and naturalized. Just because there are provisions in law to grant citizenship to those born here whose parents are both not citizens, does not make them "natural-born".
According to the passage above that you quoted; either one is a native or natural born citizen OR one is an alien or foreigner. Only an alien or foreigner can be naturalized.
One who is born a citizen is neither a foreigner or an alien, and is not naturalized but born a citizen due to natural allegiance at birth - there is nothing to “naturalize” about them.
The U.S. Constitution only mentions or envisions THREE types of U.S. citizen. Those at the time of the ratification, those who are natural born citizens, and those that are naturalized as citizens.
U.S. law reflects this and mentions, over and over again - “born or naturalized as a citizen”.
Currently one is either born a citizen or one must be naturalized as a citizen.
One who has natural allegiance at birth and becomes a citizen through the natural act of being born is a “natural born citizen”; otherwise one must be “naturalized”.