The interesting thing about the fairtax idea (or any sales tax) is that it is completely avoidable. If someone was to live completely off of their own land, and grow their own food and everything, then they would never have to pay sales tax unless they decided to buy something they could not produce (like maybe an iPad, but it turns out you can live without those).
So the idea of "everyone would pay their fair share" is completely false. But it is an appealing idea, nonetheless.