Please read the link I posted above this will show you where you are wrong Insulin has a roll to play in the process
"The rate of ketogenesis depends upon the activity of three enzymes. One is hormone-sensitive lipase (or triglyceride lipase), which is found in peripheral adipocytes. The other two are acetyl CoA carboxylase and 3-hydroxy-3-methylglutaryl-CoA synthase (HMG CoA synthase), which are found in the liver. Hormone-sensitive lipase catalyzes the conversion of triglycerides to diglycerides for further degradation to the free fatty acids (lipolysis) that serve as substrates for ketogenesis. On the other hand, acetyl CoA carboxylase catalyzes the conversion of acetyl CoA to malonyl CoA, increasing the hepatic level of the primary substrate of fatty acid biosynthesis. Malonyl CoA levels vary in the liver directly according to the rate of fatty acid synthesis and inversely with the rate of fatty acid oxidation. Therefore, malonyl CoA plays a pivotal role in the regulation of ketogenesis. Low levels of malonyl CoA stimulate transport of fatty acids into the mitochondria via the carnitine shuttle for oxidation to ketone bodies (see lipolysis and lipogenesis for details). Malonyl CoA normally inhibits carnitine palmitoyltransferase , the enzyme that transports fatty acyl CoA across the mitochondrial membrane.
Hormone-sensitive lipase and acetyl CoA carboxylase, are exquisitely controlled by the level of circulating insulin (which acts to inhibit ketogenesis), and epinephrine and glucagon (which act to stimulate ketogenesis). Thus in fasting or diabetes the high levels of glucagon and low levels of insulin favor ketogenesis through the promotion of lipolysis in the adipocyte and the stimulation of fatty acid oxidation in the liver
Insulin inhibits lipolysis and ketogenesis and stimulates lipogenesis by triggering the inhibitory dephosphorylation of hormone-sensitive lipase and the activating dephosphorylation of acetyl CoA carboxylase. In the adipocytes, dephosphorylation of hormone-sensitive lipase inhibits the breakdown of triglycerides to fatty acids and glycerol, the rate-limiting step in the release of free fatty acids (lipolysis) from the adipocyte. This thereby reduces the amount of substrate that is available to generate acetyl CoA (via fatty acid oxidation) for ketogenesis. In addition, insulin-mediated dephosphorylation of inhibitory sites on hepatic acetyl CoA carboxylase increases the production of malonyl CoA and simultaneously reduces the rate at which fatty acids can enter hepatic mitochondria for oxidation and ketone body production"