In the US Department of State Foreign Affairs Manual Volume 7, at 7 FAM 1441.3 "Role of the Consular Officer," (page 4 of the pdf) it says that, "The consular officer is responsible for adjudication of a U.S. citizenship claim for applicants for a Form FS-240 ..." That is the Consular Record of Birth Abroad. The predecessor to FS-240 was FS-545. Cruz would have an FS-545 if his mom and/or dad applied for one before they left Canada.
My point though, is that the claim was adjudicated.
7 FAM 1100 is also informative, although not an authority. In other words, it restates the legal authority, but is not itself the legal authority.
7 FAM 1113 probes the legal definition of "not included in the meaning of 'in the United States'" I point it out just because it is interesting, not becuase it has bearing on the Cruz case.
Crba is a certification of the birth. Naturalization does not deliver a crba.