Why do cats cover up their poop after going potty?

I have worked with feral cats (these are cats who have been born outside and lived on the streets their whole lives - never been pets), and every one of them will cover his or her leftover food. I believe that it is an instinct that comes from the need to hide their food from other animals - both because another animal may eat it, and also because the other animal would then know where the cat lived.