I suspect rats and mice populations are controlled largely by the amount of available food, so predation by cats or owls makes negligable difference, and just lets another rat or mouse take up the vacant niche.
I can't really see any value in poisoning or trapping rats outside in any case, just seems sensless to be honest, but I'm not especially bothered if the cat harvests as many as she wants - providing she doesn't let live ones loose in the kitchen !