Bodies can run on ketones (byproduct of breaking down fats) or glucose. I'm not sure where you got the information that T2 is related to fat heavy diet, that is not true at all. It can be related to bring fat, for to complications with obesity. It is related to glucose spikes, which causes insulin spikes, but the T2s body is insulin resistant and so sugar and insulin stay in the blood stream and can't be utilized. High sugar in the blood is the cause of most T2 chronic issues.

Also of note, a recent study has found that ingestion of cholesterol does not correlate with how much is in your blood.