Implying blame on the owners of these pets for a plague of predators way outside the scope of any natural population they would have in an area is also just off the rocker. We live in a modified environment largely of our creation, where many wild animal populations have long since slid from whatever would have in some distant past been natural. Culling coyotes in urban areas, where they can be a real danger to both pets and kids, is not some sort of grotesque ecological sin.
You're talking about humans, right?
Also, in our case, whatever our sustainable population in a place is, that's our natural population. Seeing as how we're completely a product of nature too, the numbers we can keep alive are natural.
An exaggerated coyote population in an urban landscape on the other hand, isn't natural because it depends on our presence to stay that way.