Thus, depletion of your glycogen stores results in the loss of 2.0 - 2.5 kilograms (4.4 - 5.5 pounds) of "water (and glycogen) weight" within the first week of a low-carb diet. Larger individuals often retain even more glycogen and water, which can result in immediate losses of 6 kilograms (13.2 pounds) or more.
His point is that some studies, particularly short term studies, do not account for this non-fat weight loss.
See: https://www.ncbi.nlm.nih.gov/pubmed/1454084
Discrepancy between self-reported and actual caloric intake and exercise in obese subjects.
Also, switching to a diet higher in protein tends to make people eat less calories and consequently lose fat.
https://www.ncbi.nlm.nih.gov/pubmed/16002798
An increase in dietary protein from 15% to 30% of energy at a constant carbohydrate intake produces a sustained decrease in ad libitum caloric intake that may be mediated by increased central nervous system leptin sensitivity and results in significant weight loss. This anorexic effect of protein may contribute to the weight loss produced by low-carbohydrate diets.
So in reality, the reasonable explanation is that you decreased your calories involuntary by upping your protein intake.
Are their studies that demonstrate that consuming more calories (with different composition such as HFLC) leads to weight loss compared to lesser calories (regardless of composition)?