If a person belongs to a small family branch of a famous person, can they rightfully claim to be the great-grandchild of that famous person?

In my place there is a TV show that is similar to American shows like American Idols or The Voice. In one episode a candidate, after finishing his performance and greatly impressing the judges, claimed to be the 8th generation great-grandchild of a very famous 17th century poet. It sounded pretty legit since they had the same surname as the poet, but that surname isn’t enough to prove anything. First off, the surename isn’t common but it isn’t rare either. Secondly, I have been digging for information on the poet on the net and there is no record of the man ever having a wife or children.

I have this theory: the poet might have had some relative, or even a brother (information about his early life is pretty fuzzy so things like that is quite possible). So supposedly, the branch of the family tree with him in it ended with him, but the branch of the relative or the brother continued to grow, and at some point it comes to the above-mentioned candidate. But even if that is the case, I can’t understand why he could blatantly claimed the poet to be his great-grandpa. After all the only connection of the poet to the candidate is a long lost relative. The family branch of the poet and the candidate stopped meeting after that point. It just doesn’t feel so right to me.

So is it possible that the candidate’s claim is valid, or is it just another stunt to shock the viewers? Apparently everyone believed him immediately and his claim was all over the newspapers for quite a while.