There is a basic problem with the author’s argument. While it is true that up until 1977 Canada did not allow dual citizenship, that only applied to naturalized citizens. In other words, if you moved there as a US citizen and wanted to become a Canadian citizen, you had to renounce your US citizenship first. After 1977, that was no longer necessary.
However, Canada considered Ted Cruz a Canadian citizen because he was born there, and the US considered him a US citizen because his mother was a US citizen. The Canadian law had no effect on US citizenship and vice versa. So whether or not Canadian law recognized dual citizenship at the time is meaningless - we don’t allow other countries to determine who is and is not a US citizen.
Of course that law may be why Cruz didn’t realize he was actually also a Canadian citizen until later - since he was a US citizen by birth, and at the time Canadian law did not recognize dual citizenship, why would he need to renounce a citizenship that Canada didn’t recognize?
The US would not know he was a citizen unless his parents filed a CRBA on him when He was born. That is the purpose of that form, to regiater US citizenship for somebody who is born in another country. My parents had to do one on me when I was born and I had to do one on my kids born in Germany.