http://www.mapleleafweb.com/old/features/general/citizenship/canada-first-citizenship-act.htmlCitizenship law of 1947 (In effect until 1977. Ted Cruz born in 1970) It did not permit dual/multiple citizenships. Canadians who chose to become citizens of another country had to renounce their Canadian citizenship. This was not all that unusual. Today, many countries still do not permit individuals to have dual or multiple citizenships, or only allow individuals to maintain dual citizenship until they reach a certain age (at which time they must choose which country’s citizenship they wish to keep).
The dual citizenship rule was a big problem for Canada that resulted in the "Lost Canadians" that subsequent law fixed.
The expectation, however, was that Canadians did not have dual citizenship.
And, as your quote says, there was no formal "proof" required. That implies that the expectation was still there.
It's like going to the voting booth. There might not be "proof" required, like an ID, but the expectation is that your are to be a resident of that state. MOST understand that and comply.