Epsom Salt will dilate the sphincter muscle that opens the bile duct to the intestinal tract.

That was never in question.  Magnesium is a natural calcium blocker so it helps to relax smooth muscle.  

What has been in question are the claims by so many "liver flush" supporters that they are passing "gallstones" that 1.  Are not real gallstones and  2. That are considerably larger than the ducts are capable of expanding no matter how much magnesium sulfate is ingested.  In other words, what they are passing are not gallstones, they are soap stones created by the "flush" itself.