The effect here seems to have little to do with gut microbiota: acetic acid itself induces the liver to stop making fats (lipogenesis) and start liberating fats into the blood (lipolysis). AcOH also by itself seems to decrease insulin resistance/increase insulin sensitivity, as well as downregulate gluconeogenesis. Several of the other studies in the bibliography confirmed this, and a couple even did tissue biopsies pre during and post to assess for changes in genetic expression of things like AMPK.