It's just one part of the process. Some of the most recent research is done at Newcastle University. They have kindly made their paper
Type 2 Diabetes Etiology and Reversibility publically available.
You are right with what you say; from the paper:
"However, because the process of de novo lipogenesis is stimulated by higher insulin levels, the scene is set for hepatic fat accumulation. Excess fat deposition in the liver is present before the onset of classical type 2 diabetes, and in established type 2 diabetes, liver fat is supranormal."
This is not obesity though, it's fatty liver. Most obese people don't have diabetes, what you need is a fatty liver.
The question then becomes why does the insulin metabolism change in the first place
? The answer it seems is that;
"The accumulation of fat in liver and secondarily in the pancreas will lead to self-reinforcing cycles that interact to bring about type 2 diabetes. Fatty liver leads to impaired fasting glucose metabolism and increases export of VLDL triacylglycerol, which increases fat delivery to all tissues, including the islets." It is this process that creates the inityial increase in insulin production, but then,
"The liver and pancreas cycles drive onward after diagnosis with steadily decreasing β-cell function." which results in a decrease of insulin. Basically your β-cells become metabolically inhibited and eventually die and you produce less and less and why some people have to inject it.
See in particular the section, The twin cycle hypothesis of etiology of type 2 diabetes.