You're treating this sample-is-the-population issue as if it's resolved in the statistics literature. It is not. Gelman has written on this [1][2], as the issue comes up in political science data frequently. As Gelman points out, 50 states are not a sample of states—it's the entire population. Similarly, the Correlates of War [3] data is every militarized international dispute between 1816-2007 that fits certain criteria—it too is not a sample but the entire population.
Treating his population as a large sample of a process that's uncertain or noisy and then applying frequentist statistics is not inherently wrong in the way you say it is. It may be that there's a better way to model the uncertainty in the process than treating the population as a sample, but that's a different point than the one you make.
Treating his population as a large sample of a process that's uncertain or noisy and then applying frequentist statistics is not inherently wrong in the way you say it is. It may be that there's a better way to model the uncertainty in the process than treating the population as a sample, but that's a different point than the one you make.
[1]: http://andrewgelman.com/2009/07/03/how_does_statis/
[2]: http://www.stat.columbia.edu/~gelman/research/published/econ... (see finite population section)