It's still effectively possible for someone to only have 1 kid that had a child that had a child etc. Each link could have multiple children as long as none of those descendants had children that survived to the present day.
This becomes more likely if you include genocides that may have quipped out large swaths of someones descendants.
You also have rather insular groups where a few thousand people may be largely segregated from the rest the world. That's not going to be particularly stable over hundreds of years, but you only need 1.
But as you go back in time, it becomes increasingly unlikely. At some point it is so unlikely it can be disregarded. And the point of the article is that point is closer in history than you might expect.
This becomes more likely if you include genocides that may have quipped out large swaths of someones descendants.
You also have rather insular groups where a few thousand people may be largely segregated from the rest the world. That's not going to be particularly stable over hundreds of years, but you only need 1.