The post you are responding to does not make the claim that it builds muscle, nor does it make reference to lean muscle mass... It says "preserves" muscle (comparable to "maintenance" as you suggested).
Muscle simply doesn't consume much more energy at idle than fat does but is far more useful and far less calorie-dense. A pound of muscle burns 4-6 calories per day at idle vs a pound of fat which burns 2-3 calories. Basically the same.
I would predict that the body would consume both, in a ratio that shifts from fat towards muscle as energy supplies dwindle, in an attempt to stretch the final reserves by reducing consumption.
[1] https://pubmed.ncbi.nlm.nih.gov/11086655/
[2] https://diabetesjournals.org/diabetes/article/50/1/96/10905/...
it's in fact the other way around. The body first reduces what is not used (unused muscles) and then energy reserves.
common sense
Try to build some muscle and get shredded... should be very easy with your methode/logic
If you just want an anecdote it certainly works for this guy [1]. And he, in turn links out to a ton of studies.
To be clear at no point did I claim that fasting would grow muscle, I don't have any data to back that up. What I said was that your body will preserve muscle when fasting because muscle is useful and fat is not. This is backed up by the articles I cited indicating significant HGH increase, and articles citing the role of HGH as inhibiting the breakdown of muscle and promoting the breakdown of fat.
Your claim requires evidence.