We feed our chickens our kitchen scraps and leftovers. We also house them under our apple trees so they can catch any windfall and eat any bugs or rodents that arrive. We move the straw out of the rabbit runs and put it into a container in the chicken run, so the chickens also pick the seeds and bugs out of there, too, and start the composting process so all that material can get recycled. They also fertilize our apple trees with their waste, and the compost that comes out of this process is used in our gardens.
So the chickens pretty much take care of themselves... lets talk the next step up - the rabbits. They feed on the grass and other plants that grow in our fields, as we move their mobile runs around the property. We also provide them with straw and alfalfa that has been locally grown. (We do buy that from one of our neighbors.)
So yes, we do feed our animals - but a lot less than one might think, and most of it comes from our own land. We take advantage of materials that would otherwise be waste, and use them to have a more sustainable operation. It will always be true that the same amount of resources could produce more plants (if your gardens grow perfectly)... that math is inarguable. But if you build a full ecosystem around your animals, you can do fairly well.