The abstract says, "A low-carbohydrate (<40 g/d) or low-fat ( >30% of daily energy intake from total fat [>7% saturated fat]) diet.".
If I am reading this correctly the low carbohydrate diets only had 40 grams of carbohydrate, or less, per day. This is a major change from the typical American diet, one medium size potato contains about 40 grams of carbohydrate. With such a low bar the usual habit of eating lots of bread, pasta, potatoes and rice is not possible and you really have to try changing your diet. As one of the major failings of the modern Western diet is too much processed, simple to digest carbohydrates the changes they made were probably exactly the right ones to make.
While the low fat diet stipulates less than 30% fat, the average American diet gets about 35% of their calories from fat. I can imagine that these people only slightly tweaked their diet. Maybe they ate as before but consumed lower fat versions of the same meals, a recipe to eat more sugars and other processed carbohydrates.
So I am not convinced by the simple description that this study shows more fat is better, I think it is really shows that too many simple carbohydrates are bad.
Well that is how I read the study, what actually happened may be different.