I think it fits perfectly, and it doesn't need expansion or redefinition. It's for families. Immediate families. Parents and their children. If this doesn't apply to someone, then IT doesn't apply to someone. Not everything has to apply to everyone, and the definitions do not need to be changed just because someone can't find a way to apply something to themselves.
My sibling and parents are my immediate family. Yet here I am, sharing storage and a Fantastical+Flighty family plan, and my other family members still can’t just buy their own stupid iAPs. It doesn’t make sense.