I think there's a problem with this. None of the components of the "privileged viewpoint" you invoke have any influence on Carter's argument: it therefore doesn't matter whether or not sampling is random with regard to these components.
1) Carter's argument applies whatever the shape of the population curve (flat, exponential, declining, bell-shaped).
2) Carter's argument applies whether or not the population under consideration knows about it (we could apply it to a population of lemmings, for instance).
3) Carter's argument applies whether or not the population under consideration is technological.

You may well be correct that it's no accident we find ourselves understanding Carter at a time when population growth turns his prediction into a "Catastrophe". But Carter's argument is merely a statistical observation, and it is no less true during periods of of stable population, when it predicts a long future life-span for the population.
So I think you're indicating why the "Catastrophe" aspect maybe shouldn't surprise us, but I don't think you're undermining Carter's reasoning.

Grant Hutchison