Hair splitting and Word Games. I think the Supreme Court summed up the point succinctly in Wong Kim Ark.
A person born out of the jurisdiction of the United States can only become a citizen by being naturalized,...by authority of Congress, exercised ... by declaring certain classes of persons to be citizens, as in the enactments conferring citizenship upon foreign-born children of citizens...
The Supreme court just out and out says that when Congress gives citizenship to the foreign born children of citizens, it constitutes "naturalization."
It will be interesting to see if the same Supreme Court decision that is primarily responsible for Barack Obama being ruled eligible is used to rule Ted Cruz ineligible: Honolulu versus Calgary.
I wonder if Senator Cruz was ever issued a Certificate of Naturalization.