You've kind of just explained exactly why I wouldn't be so sure that it was a mistake. Being made of something doesn't mean that it can't harm you. We're made of meat, but we probably wouldn't like getting hit by a side of beef.
It's possible that having a quantity of foreign material, even of the same element, forced through the material of the spirit disrupts the cohesion of it to some degree. A water elemental hit with a high-pressure hose might find the water it brought through from the metaplanes to make up its body getting scattered about, for instance.
Then again, it also doesn't really say anywhere that mundane fire/electricity/etc. gets to ignore Immunity to Normal Weapons unless it satisfies an Allergy. ITNW specifically says that it applies against attacks that are
non-magical, and makes no exceptions for elemental effects; otherwise, water spirits wouldn't need to list "Fire" as an Allergy. The only advantage they would have would be that some of the elemental effects reduce armor by half, and ITNW is treated like armor.