According to this Reuters story, researchers had two groups of women. One group was instructed to eat a low-carbohydrate diet. The other was intructed to eat a diet free of animal products including, meat, eggs, and milk. Even though the vegan group had no portion restrictions, they ended up losing significantly more weight.
Researchers found that of 64 postmenopausal, overweight women, those assigned to follow a low-fat vegan diet for 14 weeks lost an average of 13 pounds, compared with a weight loss of about 8 pounds among women who followed a standard low-cholesterol diet.
The weight loss came despite the fact that the women were given no limits on their portion sizes or daily calories -- and despite the fact that the vegan diet boosted their carbohydrate intake.
Please note, Dr. Fuhrman's diet, as described in his books, isn't vegan, and isn't even necessarily vegetarian. But his diet does involve a lot of the same healthy foods that the women in the vegan group of this study reported eating, including vegetables, beans, fruit, and nuts.
CORRECTION: In the first paragraph, I should have said low-cholesterol. My mistake, and thanks for the comment catching it. (The confusion came from the the line saying the vegan diet "boosted their carbohydrate intake.")