If you do a search for 'gallstone low fat', then you'll see that there is actually a lot of research that suggests that low fat diets can cause gallstones (as well as a range of other problems). The Atkins diet mentioned above is actually a high fat diet, not a low fat diet at all and yet helps people lose weight.
Basically the body uses bile to process fat and this uses up the bile that the body naturally produces. If it's not used, then it gradually accumulates and becomes a sort of sludge, which over time becomes larger and larger gallstones.
To convert fat you eat into fat on the body, the body also has to do a lot of processing, which uses energy (which in itself burns fat). The body can actually far more easily convert sugar into fat than it can fat into fat.
If you do some research on the Atkins diet, the Ketogenic diet (a high fat diet that has good success at curing Epilepsy) and low and high fat diets generally, you'll find lots of studies and research that backs this up!