No, it is not the interpretation that’s the issue.
It’s the plain text question of authority over naturalization. That is to Congress. No matter what you say it means or I say it means, it is Congress given the authority to decide that and make law based on those decisions.
The laws passed by Congress (and signed by a president or which become law by the override of the president’s veto ) are “the Supreme Law of the Land” according to Article VI of the Constitution.
The law of the land states in Title 8, Section 1401 of the U.S. Code of Laws that a “National and Citizen of the United States At Birth” includes: “a person born outside the geographical limits of the United States and its outlying possessions [like Ted Cruz who was born in Calgary, Alberta, Canada] of parents one of whom is an alien [like Ted Cruz’s father who was a Cuban citizen prior to becoming a naturalized U.S. citizen], and the other a citizen of the United States [like Ted Cruz’s mother who was born in Delaware] who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen years...” [Ted Cruz’s mother lived her whole life in the U.S. prior to moving to Canada with her husband for five years].