I just wrote a youtube comment about diabetes and realized that I haven't yet made a compilation on it. Here, then, is a taste. Diabetes is caused by fatty molecules that infiltrate muscle and other cells and interfere with the function of insulin. In particular, ceramides, a fatty molecule, is the prime culprit for insulin resistance. However, not all fats are equally suspect. Long-chain saturated fatty acids (LCSFAs) induce acute (rapid) postprandial (after meal) insulin resistance. Long term, the claim holds true, but studies need good controls since exercise and weight loss can, at least partially, burn off the problematic molecules. I will have to discuss the pathogenesis of diabetes at a later date. For now, here are some controlled trials.
Type 1 diabetics in a crossover design, when given identical carbohydrates and protein content, saturated fat results in needing to inject more insulin AND having greater glucose levels. This is strong clinical evidence that not only supports the link between saturated fat and diabetes, but demonstrates that a single meal containing saturated fat results in postprandial insulin resistance. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3609492/
Increased insulin was also found in healthy post-menopausal women, but the insulin spike was dramatic enough to prevent excessive hyperglycemia. Control groups were unsaturated fat. https://www.ncbi.nlm.nih.gov/pubmed/12493085
The same was found for non-insulin-dependent diabetes. Butter increased insulin spike, but olive oil did not. https://www.ncbi.nlm.nih.gov/pubmed/8561067
Likewise, a meta analysis of randomized controlled trials found that replacing animal protein with plant protein improved glycemic control in diabetics. http://www.mdpi.com/20726643/7/12/5509/htm
I have mechanistic and other data available. My research notes on saturated fat can be found here (does not include all research I've done, but a good chunk of it).