There is absolutely no grey area whatsoever.
The right to work and study in Canada is explicitly
denied to Foreign Nationals under S.30(1) of the Immigration and Refugee Protection Act, which is the law that governs all immigration and movement of foreign nationals into Canada.
After that explicit denial, there are exceptions carved out where an officer
may authorize a foreign national to work or study in Canada if certain conditions are met. The default position is simply a denial.
As a foreign national, you have been granted the privilege to study in Canada (and your wife to work) under certain specific conditions. If you do not meet those conditions, your study and work privileges can be immediately revoked.
In addition, you have not yet been permitted to enter Canada. You have a document that allows you to arrive at the border and ask for permission to enter. The CBSA officer has the authority to cancel that document and send you right back - you cannot assert any right to enter. Only citizens, PRs, and First Nations people have the
absolute right to enter Canada.
Here's the official word from the government of Canada
The admission of foreign nationals into Canada as temporary residents is a privilege, not a right.
https://www.canada.ca/en/immigratio...s/temporary-residents/visitors/what-visa.html
Do people with study permits get turned away at the border? No, not usually, but it's not unheard of. Naturally your chances of that happening are extremely low, but that's not the same thing as believing that you have rights that you actually don't have.
Anyway, you do what you feel is right.