[bonoboTP]

Exactly. There is an interpretation where the "population" is interpreted as a mathematical ideal process (with potentially infinite information content) and any real, physical manifestation is considered a "sample".

The old-school interpretation is stricter and considers both the "population" and the "sample" to be physical real things. It's understandable because these methods were developed for statistics about human populations (note the origin of the terminology), medical studies etc. (The word "statistics" itself derives from "state").

Somehow, frequentist statisticians are usually very conservative and set in one way of thinking and do not even like to entertain an alternative interpretation or paradigm... I'm not sure why it is so.