That paper asks these two questions:

If we're very very careful not to be fooled by the first word "fundamental", we can easily see the blatant bias of those two so-called fundamental questions. The first question assumes that specific mass is a cause of anything. The second questions is closer to being fundamental, unfortunately it's the second question, it's being set up to fail by the first question's bias. That paper cannot tell us anything. I'll rephrase the questions to illustrate.

(1) What are the determinants (i.e. the cause of) of fat and lean tissue a priori, before starvation, and do these determinants also act after starvation?
(2) Why is fat recovered faster than lean tissue, and is this related to the determinants in the first question?

Now I'll answer the second question first because it's the most obvious and the simplest. The gut is not storage, it's processing. Storage is fat tissue, the liver, lean tissue though this is not strictly storage because there is no protein storage organ like fat tissue for fat (in the form of triglycerides) and the liver for glucose (in the form of glycogen). So, tissue recovery rate is determined first by processing rate, then integration of gut output into storage organs and tissues. Quickest by far is glucose into the liver, with a large part of the meal bolus of insulin being captured by the liver on the first and subsequent passes until normalization. Second quickest is fat tissue, also with insulin being the primary regulator, incidentally using glucose as the primary substrate for formation of triglycerides - glucose -> glycerol -> esterification -> triglycerides -> fat can't get out cuz too big to fit through cell membrane -> effective storage. Slowest is lean tissue, because here it's not merely a question of one or two steps, but multiple steps in synthesis of various proteins, i.e. it takes time. Conversely, these rates are also mirrored when tissues get depleted, so that the liver depletes its glycogen stores the quickest, fat tissue depletes its fat stores second quickest, and lean tissue depletes its protein stores the slowest.

The answer above is incomplete, it doesn't tell why. The why is in the hormones and enzymes that perform all this storage and synthesis and so forth. The first and most powerful is growth hormone, acting on everything, including fat tissue. The second is insulin, primarily acting on the liver and fat tissue. These hormones act on enzymes like follistatin for muscle and lipoprotein lipase for fat tissue. However, insulin is even more powerful in that it can literally shut down growth hormone, at least until insulin has done its job, then things can return back to normal.

Now to explain why this answer is more correct. In the paper, it's basically asking which tissue mass is most disruptive, i.e. the bigger it is the greater its effect. Well, if that's the question, they found the wrong answer. Growth hormone, the most potent agent bar none, is stored and secreted by the tinest of all organs - the pituitary. The second most potent agent is also stored and secreted by a quite small organ - the pancreas. So, if the question is "what's the most potent tissue or organ", then the answer is "the pituitary and the pancreas". These two tiny little things are in fact the most potent determinants of all growth. We can even put them in direct opposition and plot a direct 1:1 correlation with what we call fuel partitioning, where for example if GH is higher there will be more lean tissue mass and vice versa.

Now for the how, because it makes it more clear. Everything that happens in the body, happens continuously. For example, muscles are continuously made by constant stimulus (I'm not exactly sure which stimulus here, but bear with me), then this constant stimulus is also continuously inhibited by the enzyme myostatin, which itself is continuously inhibited by another enzyme follistatin. Fat tissue is similar, where fat cells take in glucose and continuously produce glycerol as a by-product, then continuously esterify this glycerol (with free fatty acids that are also taken in) into triglycerides, then continuously break down these triglycerides back into FFAs and glycerol, there is non-stop back-and-forth action going on in there. And for all tissues regardless of type, everything from which we are made like amino acids, is constantly recycled in a process called chaperone-mediated autophagy (CMA) and likely other similar processes, where corrupted proteins are broken down into its constituents. The point here is that when hormones do their thing, they do it by acting on those continuous processes one way or another to shift the balance one way or another.

Now to explain why they found that the bigger tissues have the greater effect. Fat tissue is composed of many fat cells. Each fat cell contains a particular amount of fat. Thus, we calculate total fat mass ( fat cell capacity X number of fat cells ). Considering the above continuous processes, and considering that all cells contribute to the total process output, it follows that the greater the number of cells, the greater the total output, therefore the greater the mass of same cells (i.e. fat tissue is all fat cells, muscle tissue is all muscles cells, etc) the greater the effect directly related to this specific type of tissue. Simply, the more fat tissue we have before starvation, the quicker and bigger fat tissue will be during and after recovery.

I wanted to make an analogy with cars, where for example we take out parts, then put parts back in, then ask how is the car going to look after that? Well, the parts we put back in is pretty much determined by whether they fit or not, and this is pretty much determined by the initial car design by some engineer and whatnots. The point here is that the parts we put back in isn't determined by the parts we took out, but by the engineer who designed the car to begin with. But then we could argue that in biology, the designer is DNA, and that would be somewhat true. With a car again, we can decide that we want different parts, different colors, more performance this time around, a bigger engine - we can do all of that, we know how. In biology, it's the same thing, we can grow bigger muscles, bigger fat tissue, bigger whatever, in spite of the initial design. But in fact, it's not in spite of, but allowed by the initial design - DNA includes all the tools needed for all growth, including subsequent growth after puberty for example. But then again, DNA can be tampered with through epigenetics where the initial design - and the tools derived from this - are different so that the end-product of a recovery for example will be different from the original pre-starvation, as a consequence of both the environmental agents during starvation and during recovery. Again with the car analogy, "oh, my car is missing parts, and it's broken so factory parts won't fit unless I fix it first", then "well, Ima replace the parts, repair the broken stuff, but use different or better parts, and fix it as best as I know though not necessarily exactly as original, etc".

Anyways, take another look at the title of that paper, see if it actually makes any sense. To me, it doesn't. Let me illustrate. We know all about calories and the First Law, but we have no clue why biology behaves as if it didn't know all about calories and the First Law, so we gonna literally reformulate CICO in as many different ways as we can think of cuz we just don't want to even think of any other competing hypothesis. In other words, the "theory of autoregulation of body composition" is merely CICO rephrased.

-edit- As I was reading this again, I realized that the two questions I reformulated are in fact the same question. Basically, the answer I gave for the second also fits the first.