Neither. Once it's a ketone, the liver won't metabolize it. With coconut oil or butter--the ketones won't be produced unless the liver metabolizes the fat--leaving the potential for cholesterol production, etc., in the process of breaking down the fat while producing the ketones. Of course that depends on whether their explanation for the decrease is correct--that it's caused by decreased substrate availability in the liver--rather than there being some sort of signalling cascade that reduces cholesterol production in the liver, responsive to ketones.

There might be trace amounts of ketone in food, but nothing like supplementation.

One potentially nice thing here is that while the ketones might be decreasing cholesterol production in the liver itself, they have the potential to provide substrate for cholesterol production in other parts of the body, like the brain.

It will be interesting to see, when the group later releases a longer paper, what happened to people's insulin levels in the study.