This is a very complex methodology, but here's what I understood from this paper.

They enrolled 8 healthy males between 22-35 years of age with a normal BMI.

Gave everyone a Growth Hormone infusion.

Then one-half of the subjects got Ketones (betaOHB) and the other half got saline (control group) as an intravenous infusion. There were 2 visits a month apart and each person got a chance to be in each group (that's the crossover design).

Growth Hormone increases Free Fatty Acids (FFA) in your body by breaking down fat (lipolysis), but if a participant was in the Ketone infusion group, their serum FFA became markedly lower during betaOHB (Ketone) infusion even after getting the Growth Hormone. The study found that Ketones block the breakdown of fat through binding to HCA2 receptor.

During the betaOHB infusion, lots of Ketones entered the skeletal muscle tissue and promoted glucose uptake, which increases insulin sensitivity in the skeletal muscle. Also the betaOHB that entered the skeletal muscle was immediately converted to Acetoacetate and entered Krebs Cycle.

Bottomline: Having extra ketones promotes uptake of glucose by muscle, which lowers your blood glucose level and improves your insulin sensitivity.