I think this is an artifact of captivity. It's true that in the wild, tortoises sometimes do eat the dung of other animals (like goats). Although this can be nutritious, it can also lead to infection by parasites, so in captivity it is to be discouraged.
As for pooping or peeing on their food, though, I don't think this would happen in the wild. In nature, tortoises walk around from plant to plant, eliminating waste from time to time - usually when they come across a source of water, like a rain puddle. But they would rarely defecate or urinate on their own food, simply because the plants they eat would be erect.
My female Russian tortoise does poop and pee on her food sometimes (although, interestingly, the male hardly ever does this). But I think this is just because it's in a dish, so when she gets into the dish, her waste gets onto her food. When this happens, I take her out of the dish, throw away the soiled food, and either let her eat the stuff that's still clean, or else get her some new stuff.
So, I don't think it's healthy for a tortoise to be regularly eating its own waste. It may happen pretty often in captivity, but that doesn't mean they're adapted to feeding that way.
I always have to do a poop patrol in the backyard really good because I always catch my leopard tortoise trying to eat my dogs poop. It's really nasty.