My hypothesis is that Le Fay is a native from the world they're in, but she spent her childhood and early adulthood in Earth due to a portal (Avalon). Eventually she made it back (probably forced) and misses the place. This fits somewhat well the mythological Avalon, as it has no definite place in the British islands anyway. (As well as the fact she just lumps Brits all together. Also no mentions to chippy or curry.)
On haggis: I'm certain Saburou could pull it out if Le Fay described him how to prepare it - the basis is simple, oatmeal with sheep offal cooked in a sheep stomach, served with mashed potatoes and mashed rutabagas. Getting it right is tough because you need to clean the offal properly and balance it with less strong-tasting meats (e.g. stewing beef), but Saburou kitchen knowledge applies here too, no matter if it's Japanese or Scottish food.