If you listen to BioJacked #2 (the one about Autophagy), Kiefer gives the answer.
Basically, there aren't enough studies directly on IF to produce the conclusions. Kiefer had to connect the dots among studies that aren't directly about IF but study similar endocrinological phenomena, as well as delve one level deeper into biochemistry, to come to his conclusions.
So there is not "direct proof" of what you're referring to, because no one has done the direct experiments to try these things out. "Proof" is a slippery concept in science anyway...