My favorite nonsensical category 4 classification is anything with achiote in it. It's not part of a traditional European diet, and it's often used to add color so it makes the list, despite saffron having a similar role in European food and booth being a traditional and completely unprocessed ingredient.

Speaking of Mesoamerican ingredients, nixtamal is pretty heavily processed, and is a staple in many areas, but it's much healthier than unprocessed corn which can cause pellagra when used as a staple food.