This isn't an answer to your question, but it fills in the pieces missing from your quote. It is too long to post as a comment after your question.
Peter said in the comments after that post that it was MCT and not coconut oil:
Here is his comment:
I went back and checked the paper and the rats were actually gavaged with MCT, not coconut oil (sorry, the paper was peripheral to what I was thinking about). I agree MCTs are dealt completely differently from most lipids but ultimately, unless there is a major increase in heat generation, the calorie throughput on a given level of activity must be the same. The worry about the insulin spike is that it produces a few hours when HSL is inactive. OK, you'd be burning MCTs, but we could say the same about glucose replacing palmitic acid oxidation after a high carb meal (except I doubt the insulin spike is as big after MCTs as after glucose, but they didn't check this in the paper). Actually, what this suggests is logical, the body wants MCTs out of the way asap (from the way it deals with them). I can see some logic to inhibiting HSL while the MCTs are oxidised. BTW I used this paper for the MCT info.
ETA: Here is a link to the blog post and comments from which the quote in the question is excerpted:
Here is the abstract from that the link for the rat study:
Abstract Medium-chain triglycerides (MCT) induce ketosis in several mammalian species including man. To clarify the regulation of this metabolic alteration, we fed rats either MCT or long-chain triglyceride (corn oil) and then attempted to correlate ketosis with changes in (i) concentrations of selected metabolites in plasma and (ii) the synthetic and oxidative capacities of the liver. By 1 hour after MCT feeding, plasma levels of total ketone bodies had increased 18-fold, with a maximum value reached 1 hour later. By contrast, total plasma ketones in rats fed corn oil were increased only about 2-fold at 2 hours after feeding and did not exceed this value at later intervals. Hepatic concentrations of ketone bodies also increased after MCT or corn oil feeding. Although plasma concentrations of glucose decreased and insulin increased in rats fed MCT, they were not affected by corn oil feeding. MCT-induced ketosis was depressed by glucose administration. Neither MCT nor corn oil feeding impaired utilization of glucose by the liver. Hepatic lipogenesis was suppressed 50% and 90% by MCT and corn oil feeding, respectively. A marked increase of long-chain fatty acids in plasma was observed in rats fed corn oil but not in rats fed MCT. The pronounced increase of ketones in MCT-fed rats was closely related to an elevation of octanoate. In liver slices of MCT-fed rats, ketogenesis from octanoate was 10-fold higher than from palmitate, and octanoate was oxidized 4 times more rapidly than palmitate. The ketosis of MCT-fed rats was depressed by administration of 4-pentenoic acid, a potent inhibitor of fatty acid oxidation. These results support the concept that ketosis induced by MCT stems from rapid oxidation of medium-chain fatty acids. Hyperinsulinemia, hypoglycemia and depressed lipogenesis resulting from MCT feeding appear to potentiate but not initiate ketosis.
Here is a link to the full text: