As I've understood you, you've conflated a couple of things. Imposing a visa is a form of pre-screening. It works much in the way that visa applications in India and China work. The applications are given a cursory look-over, and the majority of them are refused.
Putting a visitor visa requirement on Mexico was a very effective way of staunching the refugee claimant flow, because those people just didn't get visas to come to Canada to make the claim. It's not because the legitimacy of their claim was in any way evaluated; it's just because the nature of imposing a visitor visa on a country means that very many fewer people will be showing up at the border.
So in terms of—