Homo sapiens in the Palaeolithic era would have been exposed to olives. The olive tree may have arisen from the North African tree O. chrysophylla, which existed around the entire Mediterranean Basin and the Near East. While, it’s unknown if the ancient people processed olives for the oil, the fact they were exposed to them means they ate them.
Olive oil is rich in monounsaturated fats, and diets containing monounsaturated fats have been linked to a decrease in coronary heart disease.
Like olives, Palaeolithic people were definitely exposed to coconuts and therefore coconuts can be part of the Paleo Diet. Coconut oil is rich in medium-chain triglycerides (MCTs). MCT's have several health benefits. Unlike butter or margarine, this fat is easily digested. MCTs enable your liver to quickly convert the fat to energy. By turning to energy instead of being stored, this fat will help to give you a lean healthy frame.
While it’s true that Palaeolithic people weren’t pan frying fish or cooking a steak in a little olive oil, the point of the Paleo Diet is to eat the foods that Palaeolithic people ate. Our bodies are designed to eat the foods people consumed during the Palaeolithic era.
So, if you want to follow a Paleo Diet lifestyle and you want to do a little frying, I suggest that you go with coconut oil or olive oil. Our ancestors ate both coconuts and olives, so our bodies are designed to consume these oils. Just remember not to go overboard. We may be designed to consume these products but they still have calories which can slow you down from reaching your weight loss goal.
 Friedrich W.L. (1978) Fossil plants from Weichselian interstadials, Santorini (Greece) II, published in the "Thera and the Aegean World II", London, pp 109-128,
 Keys A, Menotti A, Karvonen MJ, et al. (December 1986). "The diet and 15-year death rate in the seven countries study". Am. J. Epidemiol. 124 (6): 903–15. PMID 3776973
 Wellness Cake.com. “The Diet Cake Difference”. http://www.wellnesscake.com/the-diet-cake-difference.html