This is of course the natural analysis. An apple tree cannot produce oranges. An apple tree can only produce apples. Even if an apple tree is planted in the middle of an orange grove, it can only produce apples and never oranges. Similarly, being an American citizen, the mother of Ted Cruz produced an American citizen. The fact that she was surrounded by Canadians at the time does not change anything. As an American citizen, she produced an American citizen at birth. Mr. Cruz is thus a natural born citizen.
Cruz acquired citizenship via federal statute granting citizenship to individuals born outside the U.S. to U.S. citizen parents (Pub.L. 82–414 § 301(a)(7); 66 Stat. 236).
To retain citizenship he was required to fulfill the requirements of Pub.L. 82–414 § 301(b); 66 Stat. 236.
The retention requirements of § 301(b) where eliminated in 1978 (Pub. L. 95–432 § 1,3; 92 Stat. 1046). His citizenship is via Congressional grant, i.e. he is naturalized.
The Supreme Court is clear on this point: statutes “conferring citizenship upon foreign-born children of citizens” is naturalization (see U.S. v. Wong Kim Ark, 169 U.S. 649)
A natural born citizen does not need to take affirmative actions to retain citizenship nor can their citizenship be revoked, to the contrary, a natural born citizen must take affirmative actions to renounce citizenship. (see Afroyim v. Rusk, 387 U.S. 253).