It is not true. In fact, a low-carbohydrate, high-fat diet has been shown several times to have the potential to reverse insulin resistance in human beings. Since polyunsaturated fatty acids ingested in quantity can have a systemic inflammatory effect, the healthiest fats are saturated and monounsaturated.
A couple of things to notice in the study you cite: first, it was done on rats, and rats are very hard to get into ketosis, except at the end stages of starvation. In fact, human beings are the only mammal that enters ketosis at all easily. Second, the study was performed on rat islet cells in vitro, and results are often different from what they would be in vivo. Third, what researchers consider a “low-carbohydrate” diet is often what we on these forums would consider a high-carbohydrate diet, and the results could well be confounded by the elevated blood glucose, and not the result of the fat intake at all. In all the rat studies I’ve read about ketogenic diets for rats, the formulation given to the rats was extremely high in glucose.
So it is not entirely clear that the observed results actually apply to the pancreas of a rat eating a low-carbohydrate diet, let alone whether this rat model actually applies to human beings. The most that can be claimed on the basis of this study is that the matter warrants further study.