Isn't this a variety of the sort of "external information" we've agreed would undermine Carter if it were reliable?
Carter says nothing about how a number of different populations will behave, only about your own population.
In your scenario, each of the 10-billionth souls would conclude, according to Carter, that there was only a 5% chance they were living in the first 5% of their population.
It would turn out that 80% of them were wrong. In their own populations, that simply means that they are in the 5% pastward tail, and that the 95% of their population who come after them are correct in using Carter's reasoning.
Carter would therefore still be entirely correct and consistent within each population, although the 10-billionth souls could have made a better estimate if they'd been party to the external information your immortal alien has collected about population numbers.

Grant Hutchison