"Natural" is a question of perspective and context. What I mean by natural, is simply that the animal is fed food items that would fall into the category of things it eats in the wild. Let's look at a cow for instance. A cow grazing on grasses and weeds in a pasture is eating a natural diet because cows are grazers. Does it matter what species of grass the cow is feeding on? Not really. Cows are grazers and feed naturally on grasses of many kinds. To say that it is not eating a natural diet just because the species of grass it is eating now is not what it's ancestors ate seems too nitpicky to me. Now, most cattle ranchers feed those same cows on grain when it is close to time to slaughter and sell the meat because it makes them fat very fast. Dry grain is NOT a natural food for cows because they would never eat it in the wild. That is an example of natural vs. unatural food.
With most arid tortoises, their natural diet in the wild is grasses and green leafy weeds and the leaves and blossoms of shrubs and vines. In other words, they are grazers and leaf clippers. The closest thing to a truly natural diet you can give them in captivity is weeds that grow wildly, grasses, and blossoms from shrubs and vines. The next step down would be feeding them vegetables and green leafy greens from the store. Some people say that store-bought food is not really natural because it is not exactly the same botanical species that are found in the animal's home terrain. True, the types of vegies you get in a store isn't exactly what they would eat in the wild, but it comes close. Did you know that many types of greens and vegetables in the store are closely related to wild plants you may see growing here or in Africa or in the Medeterranean? Dandelions and sow thistle are related to lettuce, botanically speaking.
What tortoises do NOT eat in the wild is soybeans, or any kind of cooked or human-prepared pellets. That is what is meant by "unnatural" foods. These food items contain too much protein and not enough fiber. A very unhealthy combination. Desert type tortoises have highly specialized digestive systems that are made for plants and only plants.
Like I said earlier, it may take years for the health disaster to show up, and that is why it is hard to show the results of prepared foods on the health of tortoise in studies. Pyramiding is well known and is thought by most tortoise experts to mainly be the result of too much protein and not enough calcium. Human-made foods are high in protein and most contain elements which can block calcium absorbtion. What many people don't know is that pyramiding is only the "tip of the iceberg." When it occurs, there is much more damage that you cannot see in the internal organs of the animal. This rarely occurs on animals that are fed naturally and given supplemental calcium. It does not occur at all in wild specimens.