**Core Concept**
Gallstone formation is influenced by a combination of genetic, metabolic, and environmental factors. The composition of gallstones can vary, but cholesterol stones are the most common type, often associated with supersaturation of bile with cholesterol.

**Why the Correct Answer is Right**
Hypercholesterolemia, or high levels of cholesterol in the blood, is not a direct cause of gallstone formation. In fact, the relationship between cholesterol levels and gallstones is more complex. While elevated cholesterol levels can contribute to the formation of cholesterol gallstones, this is not a direct causal link. The primary factor influencing cholesterol gallstone formation is the supersaturation of bile with cholesterol, which can be influenced by various factors, including genetic predisposition, obesity, and dietary habits.

**Why Each Wrong Option is Incorrect**
**Option A:** Clofibrate therapy is actually a risk factor for gallstone formation. Clofibrate, a fibric acid derivative used to lower cholesterol levels, can increase the formation of cholesterol gallstones by altering bile composition and increasing cholesterol supersaturation.

**Option B:** Hyperalimentation, or total parenteral nutrition, can increase the risk of gallstone formation due to the high caloric and lipid content of the nutrition regimen, leading to bile stasis and supersaturation.

**Option C:** Primary biliary cirrhosis is a chronic liver disease characterized by progressive destruction of the intrahepatic bile ducts, leading to bile stasis and supersaturation. This condition is actually a risk factor for gallstone formation.

**Clinical Pearl / High-Yield Fact**
It's essential to note that the relationship between cholesterol levels and gallstone formation is complex, and other factors, such as obesity, age, and genetic predisposition, play a more significant role in the development of cholesterol gallstones.

**✓ Correct Answer: D. Hypercholesterolemia is not a primary risk factor for gallstone formation.**