Why does oil transfer heat to food more gradually than water? While working on the homework for week 2 of Harvardx's Edx course, SPU27x Science &amp; Cooking: From Haute Cuisine to Soft Matter Science, I came across this question:


  The difference in the specific heats for water and oil is important
  for cooking. For example, oil heats faster and you are less likely to
  overcook food if you cook it in oil than water. Briefly explain these
  observations, using the scientific ideas from this week.


We are asked to write a short response to it, and after submitting it, we are given a grading rubric and asked to do a self assessment. Here is my response:


  While it is true that oil heats faster than water due to its lower
  specific heat capacity, it is not true that food is less likely to be
  overcooked than water. The boiling point of oil is generally much
  higher than that of water (about 250-350 degrees Celsius compared to
  100 degrees Celsius). This means that when cooking food in oil, it is
  very likely that your food will reach temperatures much higher than if
  they were cooked in water. Knowing that a liquid's temperature stays
  constant at the boiling point, food cooked in water will never go
  beyond 100 degrees Celsius, so you are less likely to burn food in
  water than if you were to cook in oil, as the reactions that result in
  burns do not occur at that temperature, but do occur in the boiling
  point of oils.


and the rubric we are given states:


  A full answer contains at least two of the following ideas :
  
  
  Oil has a lower specific heat than water.
  Oil can be heated to high temperatures with relatively smaller input of energy than water.
  At a fixed temperature, oil transfers heat more gradually to food than water at the same temperature.
  In liquid form, oil can be heated to a higher temperature than water. 
  
  
  You may use different words to express these concepts, so judge
  your response based on the meaning of your answer, rather than
  expecting your wording to match this exactly.


So it looks like my response is quite different from the suggested answer. In particular, I am confused that the provided answer does not explicitly address whether it is true that food is less likely to overcook in oil. I am also unsure why oil transfers heat more gradually to food than does water.

I would really appreciate it if anyone could clarify my questions, and also give me some feedback on my response.
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.