True, oil is processed food. By that same argument, all cooked food is processed.
The animal fats I eat are from my own farm, processed by me, lard rendered by me. I realize not everyone can do this, but quality control (and lack of preservatives and other bullshit) is much easier to do when you're the one doing the cooking.
Just like roasting a chicken yourself is making "processed food", there's a big difference between that and, say, getting some chicken from Chili's, or some canned whole chicken.
When I speak of "processed foods" I guess what I mean is highly processed foods, usually processed in factories, surrounded by incentive structures directly opposed to healthful food production (because it's invariably more expensive).