I am of the other opinion. To me it was the depletion of the body fat that led to weight loss. On an ultra restricted diet, the body is tricked into thinking starvation is coming, so it starts raiding the body's long term stores, i,e, the lipids it secreted away for that rainy day. First it depletes the muscle stores, which is glycogen. Now glycogenis a mix of stored glucose and water, so depleting this store results directly in significant and fast weight loss as water is removed. This is how most weight loss diets work, indeed the Prof Taylor diet is the Cambridge Plan of the 80's using Optifast shakes and 800 kcal. the DIRECT plan used currently also uses the Cambridge Plan shakes again.
So initial weight loss is not what we term as body fat. Once the muscle stores are depeleted then the body raids the lipids stored in the liver (often blamed for the Dawn Phenomenon or Liver Dump) and when this runs out then the interesting stuff begins. There is a clarion call from the hormones for all good fats to come to defend the flag, so now we see adipose tissues such as the brown cells, and the pancreas and liver give up their remaining fat deposits, This is why prolonged use of this type of diet is not recommended since it leads to protein scavenging if fats are not included. That state is starvation.
Prof Taylor states in the extracted paragraphs in the OP that it is the removal of ALL body fat that does the magic. He also says the diet plan to get there is just a tool and does not have to be ultra low calorie, He used Optifast because it was a recognised diet acceptable to the NHS, and had controlled nutrition which he needed to eliminate confounders from the experiment. In other words, it was convenient.
Sorry Little Bird, it was the use of the word Reveral that we were critquing, not you. That is an emotive term. and since you were aiming this topic at newbies, it was important for us to make it clear that it is not the silver bullet or holy grail that they may be seeking. The work that Prof Taykor did and continues to do may in rime lead to that happy solution, but it is not yet in our hands, But it has given us another tool we can use.