I've thought a little bit more about this. According to Dr. Johanna Budwig sulfur, like that found in eggs, yogurt, and cottage cheese, break down oils into a water soluble state. If that is the case, then the 2 egg yolks would probably break down the 1/4 cup of oil in this recipe into a substance the liver would not recognize as oil and thus it would not contract as hard to expel bile. However, it should contract to eliminate the cholesterol.
I'm not sure why it wouldn't produce the same results except for the Epsom Salt which is supposed to relax the liver and open up the bile channels to facilitate the expulsion of stones.