In the famous Slaughter-House cases of 1872, the Supreme Court stated that this qualifying phrase was intended to exclude children of ministers, consuls, and citizens or subjects of foreign States born within the United States. This was confirmed in 1884 in another case, Elk vs. Wilkins, when citizenship was denied to an American Indian because he owed immediate allegiance to his tribe and not the United States.
If citizenship was denied to an American Indian because of divided allegiance, how can it be granted to babies born of illegal aliens, or Chinese tourist baby hotels in California?