Sure, carb intake is only one factor. It's a very important one though. Obesity and inactivity contribute a great deal, along with genetics. In essence people develop tolerance to insulin because their bodies are flooded with it, in an attempt to metabolize excess carbohydrates. Insulin resistance means the insulin stops working as effectively, resulting in the body putting out more and more, which doesn't work either, and resulting in chronic hyperglycemia. High body mass means the body has to put out more insulin to maintain a certain blood concentration. Exercise plays a role in glucose utilization, also. Over time, the islet cells get exhausted, too. Type 2 can to some extent be turned around with a low-carb diet and exercise, unlike Type 1.

I guess it depends on your definition of “directly”. Like does falling off a building directly cause death, or is that the deformation of one’s skull?

You mean eating so much sugar that your pee becomes sweet isn’t directly caused by having excessive sugar?