If the stuff coming out has been broken down by labs and found to be made up of the very same stuff you are taking then I think that's a rather strange coincidence.
I never agree with doctors (no offense), but this one is right.
This stuff does not physically go through the liver. The things your stomach breaks down and eventually absorbs through the intestine passes through the liver via the blood, but in its unbroken down state food does not go through the liver.
I don't doubt people are feeling better from this necessarily, but if the "stones" coming out are comprised of olive oil and juice and not calcified cholesterol, then it's likely that the mixture itself is building up into chunks in the intestine and on down in to the colon.