Hard "Stone"? Have you ever gotten a very hard "stone"? "Stone" that could not be cut with a kitchen knife?
Beside cholesterol, gallstones can contain protein and calcium.
Stones predominantly composed of cholesterol are never hard enough to resist cutting with a kitchen knife.
Stones predominantly composed of protein can be very hard, almost like human bones, and may resist cutting.
Stones predominantly composed of calcium can be even harder, like a stone and may even resist scratching.
Hard stones can not be cut with a knife. If you can not cut your stone with a knife, then you know the stone you got contains either a lot of protein or a lot of calcium or both.
In any case, there is no way such stone was formed overnight, from oil and digestive juices.