The first source is saying that butter delays the blood sugar and insulin curves, but does not otherwise alter them. That is important. I do believe there is an agenda against saturated and animals fats. It also states that MUFA plant and PUFA plant without much saturated fat (olive and corn) reduce the amount of insulin and the blood sugar curve, so while butter does not raise the insulin used to handle carbs, nor raise the spike (important because some out there in modern medicine claim that it reduces insulin sensitivity after a meal which it couldn't given those 2 facts), relative to Olive and Corn combined with carbs it does "raise" the insulin response and blood sugar excursion. Its odd because butter is largely Oleic. And there is evidence that myristic I think reduces insulin sensitivity but oleic increases it, so for butter they balance out. I've read that assertion in other places as well.
The second says that Lard, safflower and corn oil do not increase the insulin response which "seems to be unique to butter"