What is the relationship between data generating process and validity of inferences? This is a hypothetical example:
I was assigned a section of land in an experiment station. I divided the land into 40 plots and planted grass species A in 20 randomly selected plots and grass species B on the other 20. Seeds for both grasses were purchased at the local supplier. I measured the total mass of hay produced by each plot and analyzed the data using correct calculations and frequentists statistical procedures. The 95% confidence interval for the difference (A-B) between average hay production in ton/ha was {2.0, 2.5}. This is a big difference in practical terms.
What is the population of inference? Under what conditions should I repeat the experiment 100 times such that I can have a reasonable expectation that the mean (whose mean, by the way?) is bracketed by the 95% CI in 95 of the tests?
What would be the formal frequentist statistical basis or method by which having the data from the experiment would allow me to have a better guess of what would happen if I buy seeds from a different supplier, and or plant the grass in other section of land in the same station, and or plant the grasses another time in another place? 
 A: I'm not sure that you can just create a CI, and then ask "how is this valid?". What you need to do for the frequentist inference is 1) specify your population; 2) specify your sampling distribution (or process); 3) specify your statistic, and which population quantity it is estimating; 4) calculate the sampling distribution of this statistic; 5) invert the sampling distribution to get CI.
There is not necessarily 1 population that leads to 1 CI. You need to specify what the population is, and work through the steps.
As for using the data to help with other situations, I doubt it would be too useful, because your sample only has 1 supplier, 1 time period, 1 section, 1 station. Your sample has no variation over these, so you can't test these assumptions with your data. An analogy is if you only planted grass species A in your sample, but want to know if it's better/worse than species B. However, these essentially would form caveats for how general the (A-B) difference is. It could be that A>B for all cases, or it could be for your particular time period, or the particular supplier, etc..
The above problems would show up in part 4) where your sampling distribution would depend on quantities you have no data for (eg average hay production for species A for a different supplier in the same section, same time period, same station).
