Correct but good universities already do the screening for this if they accept you.
Highly
incorrect. They don't do screening to see if the credential you're applying for makes sense - for example, I have a Ph.D. If I went and applied for a BA degree, the university would have no issue with that. BUT if I were applying for a visa in that context, the visa officer would not think that getting a BA would be an appropriate advancement of my academic career needing a visa.
The university will make sure you meet an academic minimum standard, but as you'll be an international student, they will
happily take your money for any course you may want to take. IRCC won't necessarily agree with the university's decision.