The low carb theory on weight loss revolves on insulin's action on adipocytes. Specifically, high insulin favors deposition (esterification to form triglycerides) in the fat cells and suppresses lipolysis (breakdown to free fatty acids).
This of course is true. But the problem with this discussion is that it is incomplete. You see, lipolysis has little to do with fat burning per se. That is beta-oxidation occurring in the mitochondria in a series of cyclical reactions commonly called the Fatty Acid Spiral, FAS. Free fatty acids are constantly delivered to the cells and being taken up. Those that are not oxidized for energy are re-esterified and stored as triglycerides inside the cells (e.g. IMCL or IMCT).
Now here's the rub. As even Gary Taubes discusses in GCBC, we are continually cycling fat into and out of our fat cells with the Triglyceride/Fatty Acid Cycle. That blog post being the first mention of that infamous 2003 Reshef et. al. paper that sort of started all the mayhem here at the Asylum. In that article we learn that at all times, a considerable proportion of the fatty acids released by adipose tissue are taken back up and re-esterified - some by adipose tissue, some by peripheral cells.
This, in and of itself, tells us that we are always in a state of FFA "excess" availability. Low insulin, high insulin or everywhere in between.
The rate limiting step in fat burning is the initiating reaction of the FAS/beta-oxidation. Simply put: How many fatty acids are ultimately "burned" or oxidized, because these molecules only make it ultimately out of the body by this route.
Therefore any argument focusing on lipolysis rates as relates to availability of energy substrates or fat burning capability for the individual is simply gimmickry. What is "rate limiting" for fat loss is the degree to which your body requires fatty acids as a fuel source and the degree to which you are replenishing that which is used.