Allergy is possible, esp if your friend has similar reactions to other nightshades like eggplant. Speaking for myself, I notice a reaction when I eat smaller tomatoes that have more peel to flesh, like roma or cherry. Not spicy but more like itchy/prickly. Still eat them tho
皮蛋 is more like preserved? i.e. explicitly not rotten. That’s like saying jerky is rotten meat