**Core Concept**
Brown pigment gallstones are a type of gallstone formed due to the precipitation of bilirubin, which is a breakdown product of hemoglobin. This process is often associated with conditions that cause an increase in the concentration of bilirubin in the bile, such as biliary tract infections.

**Why the Correct Answer is Right**
Brown pigment gallstones are formed when bilirubin reacts with calcium to form calcium bilirubinate, which is then precipitated out of the bile. This process is facilitated by the presence of bacteria in the biliary tract, such as E. coli, which can break down bilirubin into its more insoluble forms. The increased concentration of bilirubin in the bile, combined with the presence of calcium, provides the ideal conditions for the formation of brown pigment gallstones.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not specify the underlying cause of brown pigment gallstones. While inflammation may contribute to the formation of gallstones, it is not the primary mechanism.
**Option B:** This option is incorrect because it is more closely associated with cholesterol gallstones, which are a different type of gallstone altogether.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that brown pigment gallstones are often associated with biliary tract infections, such as cholangitis. This is because the bacteria present in the biliary tract can contribute to the formation of these stones by breaking down bilirubin into its more insoluble forms.

**Correct Answer:** C.