The numbers of birds decline because WE destroy their ecosystem and breeding places, not because cats catch the unwary and the old, sick and weak of the species. If anything , cats help the species survive by weeding out the lesser individuals.
Also, cats make up for some of the natural predators we have eliminated or greatly reduced, such as wolves.
The Aussie people may be right....... about Australia that is. Cats are not an indigenous species down under, they have no natural enemies and upset the ecosystem. As do rabbits, horses, sheep and other animals WE introduced there.