[driftdiver]

They have

http://www.dallasnews.com/news/politics/headlines/20130818-ted-cruz-born-a-citizen-of-canada-under-the-countrys-immigration-rules.ece

“Dated a month after his birth on Dec. 22, 1970, it shows that Rafael Edward Cruz was born to Rafael Bienvenido Cruz, a “geophysical consultant” born in Matanzas, Cuba, and the former Eleanor Elizabeth Wilson, born in Wilmington, Del.

Her status made the baby a U.S. citizen at birth. For that, U.S. law required at least one parent who was a U.S. citizen who had lived for at least a decade in the United States.

She registered his birth with the U.S. consulate, Frazier said, and the future senator received a U.S. passport in 1986 ahead of a high school trip to England.”

[Ray76]

That is not a U.S. birth certificate.

[Ray76]

As I pointed out, the parents can apply for a Consular Report of Birth Abroad (CRBA). According to the article you've linked, they did apply for a CRBA and it was given.