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When talking about populations, this should be implicitly assumed - just like that the experiment took place on Earth and the participants were breathing air. I don't know why this isn't burned into peoples brains with a big flashing neon sign, and why someone inevitably comes up with a counterargument of 'but not all X' when these things are discussed.

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Because they don't want it to be true and will come up with any argument, no matter how stupid, to counter this observation.

I think that's being too cynical. Most people simply don't think in terms of integrals over probability density functions.

We organize our understanding into categories and reason about them using propositions that are either true or false.

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