Firstly, may I suggest cholesterol stones may be a better name for these soft waxy stones that can form in both the liver and gallbladder, and are composed of mostly cholesterol. With this distinction perhaps we can avoid the unnecessary confusion about why the doctor says they aren't gallstones? They are clearly a different entity, they don't show up on x-ray and don't tend to show up on ultrasound either.
Second, I have read some of the research on why these may form. Agnes compiled information years ago saying that the condition of the bile is such that the cholesterol can not stay in solution. The bile is supersaturated with cholesterol. It would make sense to me that a high cholesterol diet (and high cholesterol blood levels) would provoke this condition. This would indicate a vegan or low animal fat diet as being healthier overall.