The model is simplified. There is another more sophisticated model in which the date in which the humanity is exactly divided into two groups (those who are our direct ascendents and those who don't have descendents today) is earlier than 550 AC. There are two explanations for Gengis Khan not being the gret-...-great grandfather of said person: he either doesn't have direct descendents or because he is inside the period where the wrold doesn't divides in two said groups.
Don't be so quick to dismiss mathematical models. An outdated model such as Newton's for gravity which has around 350 years is still used to model the trajectory of satelites and probes. It is impossible, as far as we know, to prove that a mathematical model is the correct one. But that doesn't mean that its predictions aren't remarkably accurate.
He turns his mind away from those phenomena, and having done so, inclines his mind to the property of deathlessness: 'This is peace, this is exquisite — the resolution of all fabrications; the relinquishment of all acquisitions; the ending of craving; dispassion; cessation; Unbinding.'
(Jhana Sutta - Thanissaro Bhikkhu translation)