This means the diet likely had an appetite suppressing effect, not different burn efficiency. Alternatively their adjustment was not controlled for water intake

This means the diet likely had an appetite suppressing effect, not different burn efficiency. Alternatively their adjustment was not controlled for water intake or retention. Note the calories were not controlled just energy adjusted based on weight loss. So the diets were not exactly same calories. A diet that causes more water retention would be adjusted less so could potentially get more loss in the end. (Or vice versa, it is tricky.) This is all old hat but it is admirable someone reproduced earlier Cambridge studies which showed the same effect 10 years ago. Now, go out there and figure out the difference that causes appetite suppression or burn increase. Or if your methodology was junk.