Good question. The Miracle-Mineral-Supplement will clean out the liver over time, especially when combined with the other holistic cleansing steps. Eventually, everything will get cleaned out or oxidized and removed by the body, but it is very essential to keep up the hydration and move to green eating.
A Liver Flush will not hurt though, and I have been thinking of doing some myself. I have heard of the idea that the stuff that comes out is really just the stuff that went in, but then people have felt so much better afterwards. I have heard of some people who completely got rid of seasonal allergies after a few liver flushes, so that does not support the idea that what comes out is merely what went in.
Is seems to me that it is probably a combination of both: the stones coming out do contain the oil that one ingests with the flush, but also much matter that was "stuck" in the liver.