It is true that olive oil gets emulsified - but no way can it form stones. You can do the experiment for yourself - I've done it. Take olive oil in a jar add in acetic acid (vineagar), which is the same pH as the stomach (pH 4). Then add in bile acid tablets (from Walmart). Guess what? it does not solidify. HYPOTHESIS BUSTED! BAM!
Now, as to how large stones get out of the liver. My wife likes to eat beef liver, so one night I took the opportunity to look at the liver anatomy. The ducts are incredibly tough and stretchy. Also, olive oil does two things: (1) it softens the stones so they squeeze through and (2) lubricates the walls of the ducts.