The movie is mixed up about what causes type 2 diabetes. It's about insulin, not about the fat.

It goes like this:

eating the wrong diet can cause insulin overload - too high, too often
insulin overload causes insulin resistance
insulin resistance impairs the burning of glucose
Impaired glucose burning while eating the same causes excess glucose
excess glucose stays in the bloodstream and continues to rise

There's a neat science article from a while back that talks about how you can see insulin resistance years before developing type 2.

Problems in the Furnace from Howard Hughes Medical Institute

I haven't seen the movie but I seem to recall studies where they have people eat a fatty meal and then show that glucose stays high after the meal. Fat phobes think fat is the bad actor there, so one could interpret that data such that fat is the cause. Another interpretation is it was the high insulin overall from whatever the meal was, and the fat is just a bystander.