Again, not true, per 14th amendment. Also, see "anchor babies."
What you are talking about is a standard for legal residency, welfare, education and voting...and it was written to apply to freed slaves...not freeloaders.
Since you offered Wikipedia this is from the page you supplied a URL to.
There is dispute regarding whether the foreign-born children of U.S. citizens are natural born citizens.[26] One view interprets the "natural born Citizen" clause as meaning that a person either is born in the United States or is a naturalized citizen.[27][not in citation given] According to this view, in order to be a "natural born citizen," a person must be born in the United States, or possibly an incorporated territory; otherwise, they are a citizen "by law" and are therefore a "statutory citizen," (not necessarily, however, a naturalized citizen, which implies a pre-existing foreign citizenship).[26] Another view holds that the clause only requires that a president be a citizen at the time of birth, whether under the Fourteenth Amendment or under federal law.[28]
Seems like you don't even read your own cited sources.