The only problem with that is that Rafael Cruz (Ted’s father) did not become a naturalized citizen of Canada until 1973 .... three years after Sen Cruz was born.
Now we can get back to the divided allegiance issue. Even though Rafael Cruz (Ted’s father) sought and was granted asylum in the United States, Rafael Cruz moved his family to Canada and became a citizen of Canada (who would do that). It is very pertinent to understand that at in the same timeframe between 30,000 and 40,000 Viet Nam War Draft dodgers and deserters also fled to Canada which contributed to a very acrimonious environment for the parents of a so called American child to live. A person can only speculate what anti-American feelings and beliefs Cruz was exposed to at home.
Rafael Cruz was granted asylum but fled to Canada along with thousands of other reprehensible expatriates.