Why does oil transfer heat to food more gradually than water?
First, I don't think the question you are asking about is written well (your question about this question is better). We don't have the benefit of the course's context, but alone this question seems poor. The phrase "you are less likely to overcook food" is problematic because the techniques for cooking with oil and water are quite different, as would be expected based on the specific heats and boiling points. Although oil may transfer less heat over a fixed time period at the same temperature as water, it is unlikely you would have the oil and water at the same temperature. You simply don't cook with oil and water in the same way. 

In the original question and answer, the term overcook seems to refer to the core temperature of the food. Your answer considers overcooking as burning, which is not the same thing. Perhaps they are thinking of the case where your steak will not get well done (overcooked) before you notice the outside is unpleasantly charred when pan frying in oil, but boiling the steak may result in a past-well done product without visual indication.