EU institutions have argued on several occasions that national and EU citizenship should not be awarded without any genuine link with the Member State concerned. Some scholars have adopted the same position, justifying their position referring to the genuine link requirement established by the International Court of Justice in Nottebohm. This has prompted criticism from legal scholars, who point out that Nottebohm was wrong as a matter of international law and moral principle. This paper shows that supporters and critics have failed to recognise that they have been talking with different conceptions of the genuine link requirement in mind. The question of whether to apply a genuine link requirement for the recognition of nationality is altogether different from the question of whether to apply a genuine link requirement for the acquisition of nationality. Nottebohm concerns the first; the arguments of EU institutions the second. The argument of EU institutions cannot therefore be dismissed by dismissing Nottebohm. I subsequently explore the normative arguments for predicating the boundaries of national membership on a genuine link requirement. There are weighty moral reasons for member states to condition the acquisition of national and EU citizenship on the presence of a genuine link. Finally, moving from the normative to the practical, I argue that such a requirement would have far-reaching consequences (targeting not just investor citizenship schemes) and cannot be enforced as a requirement under EU law.