Elevated insulin concentrations inhibit hormone-sensitive lipase activity, thereby blocking adipose tissue lipolysis.

Study: Adipose Tissue Free Fatty Acid Storage In Vivo: Effects of Insulin Versus Niacin as a Control for Suppression of Lipolysis

Insulin tells fat cells to stop releasing fatty acids into the blood, and this study shows that when insulin is high, fewer fatty acids come out of fat tissue—meaning it’s doing exactly what the claim says it does.

Study: Suppression of systemic, intramuscular, and subcutaneous adipose tissue lipolysis by insulin in humans.

When insulin levels go up, your body stops breaking down fat in fat tissue — this study shows that clearly in humans. So high insulin means your body stops burning fat for energy.

Study: Upstream transcription factor 1 gene polymorphisms are associated with high antilipolytic insulin sensitivity and show gene–gene interactions

People with certain genes respond more strongly to insulin’s signal to stop breaking down fat, which means insulin is better at shutting off fat release — exactly what the claim says.

Study: Adipose tissue metabolism in obesity: lipase action in vivo before and after a mixed meal.

When you eat, your body releases insulin, which normally tells fat cells to stop breaking down fat. This study found that in obese people, fat cells don’t respond to insulin properly — but that doesn’t mean insulin doesn’t usually stop fat breakdown; it just means the system isn’t working right in obesity.