Sorry but that's idiotic. A common ancestor would be further removed from us than the neanderthal and all parties agree that the Neanderthal is too far removed to be an ancestor. That's like claiming that dogs are too far genetically removed from wolves to be descended from them and that, therefore, they (dogs) must be descended directly from fish.
Both of my parents are dead. There does not exist any person I could be a direct descendant of. Does that mean I have no ancestors?