Rock Soup With Edible Rock:
It is not only possible, but quite common to make rock soup wherein one eats rock and all. In fact most soup has too much rock in it, especially commercial soups. If you haven’t guessed by now the rock in question is salt. As a natural occurring mineral, I believe salt qualifies as a rock.
As far as I can determine the stone soup story goes way back into history, with many versions. This makes me wonder if the story is based on a true story, long lost in the fog of time. I can well imagine an enterprising soul with a good source of salt but little else dropping a fist sized chunk of salt into a cauldron and enticing the rest of the community to add the rest of the ingredients.
In a way, the modern versions do not make sense to me as if the rock was still there at the end, unchanged and uneaten, the providers of real ingredients would have felt cheated. All of the versions I know of end with the soup being simply wonderful and everyone quite satisfied. This would support the theory of the rock being salt. It would both disappear and add a lot of flavor to the soup…amazing everyone and starting stories that would travel with humanity through time.