That idea, 'the insulin hypothesis', has not been proven. In fact there is now evidence that claim is false. (Paywalled study [1], summary in this article [2]).
[1] http://www.nature.com/ejcn/journal/v71/n3/full/ejcn2016260a.... [2] https://www.vox.com/2016/7/6/12105660/do-low-carb-diets-work