But isn't JoostvD's point that someone can't just rock up and say, in effect, "Here I am: I'm not the citizen of an EU country but I have a durable relationship with X," where X is the citizen of another EU country — no, it will require more than just the person's say-so? That doesn't mean that it is not the right of such a person with a durable relationship to get a residence permit, or that a residence permit won't be granted, but some proof is likely to be needed.

The best advice would surely be for the OP, or the OP's partner, to contact the relevant embassy/consulate in Canada and find out, first hand, exactly what is required. That takes us back to one of the OP's original questions: which country?...