Not the OP, but in Canada at least, I think you would legally be expected to because common law is (as far as I’m aware) very nearly marriage and is entirely implied by time living together in a conjugal relationship. It might be provincial to determine the actual property laws, though.

I don’t have a firm opinion here, but I think the key difference in your case is that a conjugal relationship has some expectation of… Oh I don’t know, mutuality? A landlord tenant relationship is a lease agreement. If your roommate didn’t sign any kind of lease agreement, they might have a legal case to just not pay you and suffer no consequences (I don’t know), but they’re not in a conjugal relationship, so there’s also no implication of shared ownership.

Without signing lease agreement and being in a conjugal relationship, I think there is a pretty fair case that expecting shared ownership is a fair assumption.

That all said, it’s also really up to the individuals to figure that out early, and the deception in the meme suggests that the agency to have that discussion wasn’t available, and that’s really the part I find problematic here.