Nice source. The gallbladder is squeezing out bile, so that would make sense.
So the soft brown stones primarily form outside the kidney and the gallbladder.
So can we also say that the cholesterol and pigment stones are the hard ones that are formed in the gallbladder? It appears to describe them here:
"When you eat, your gallbladder contracts and releases bile into the common bile duct — a continuation of the hepatic and cystic ducts. The common bile duct then carries bile to the upper part of your small intestine (duodenum), where it begins to help break down the fat in your food. But if bile within your gallbladder becomes chemically unbalanced, it can form into hardened particles that eventually grow into stones. This may take several years."
So basically the soft brown stones form in the primary bile duct area, and the hard pigment and cholesterol stones form in the gallbladder(over time)?