No, no, no. Surely you jest again. Paleo dieters use unrefined oils only. All of us Paleoites know that.
My choices are coconut oil and cold pressed olive oil. Flaxseed oil is good too and is NEVER available in refined form. Of course, raw walnuts, cashews, macadamia nuts, almonds and avocados are not refined, last time I checked. Unless he uses the word "refined" the default in a comparitive list like this is "unrefined" or "cold pressed" or "natural".
With all that fat in my diet, it's amazing how I've gone from 22% body fat down to 13%. I'm a well "oiled" machine now.