I asked this question through different CBSA agents and all of them told me that it was not required to carry that card, as long as the car is a properly insured.
All of the third party websites or rental agencies could not provide the source of that requirement, so it could be outdated.
It is very interesting that you just couldn't find any information regarding the yellow card requirement from the government website, CBSA, or the Canadian Council of Insurance Regulators website.