It is quite true that my great-great-grandmother was Nellie Smith. This is a fact that is undoubtedly true and not contested by anyone who has half a brain in their skull.
However, it is also equally true that I did have a high school classmate named Maria Smith to whom I am not related. There is no connection. Do you have any idea how many billions of Smiths are living on this planet called earth? Smith is the most common name in the English language and then there are the German Schmidts who Anglicized to Smith and who knows what else. Just because someone's last name is Smith, that does not mean that I have any idea who they are or why I should care. Just having the surname Smith does not mean that we are related or that I should in any way be intimidated by Maria who is just an icky dog of whom I remember almost nothing.