No free lunch in statistics: an elaboration James et al. "An Introduction to Statistical Learning" (2013) p. 29 states:

There is no free lunch in statistics: no one method dominates all others over all possible data sets. On a particular data set, one specific method may work best, but some other method may work better on a similar but different data set.

The focus on data sets leaves an ambiguity as to whether the no free lunch phenomenon is due to
(1) random sampling from any given data generating process (DGP) or population, resulting in samples with different properties/patterns or
(2) the variety of possible DGPs and populations that are being modelled.
My understanding is that the no free lunch theorem concerns (2) rather than (1).
Quesion: Would it not be more precise and accurate to replace "data sets" with "data generating processes" in the passage?
 A: I think that the expression data set is used in a more broad sense than a single sample from a distribution. In practice, the expression data set is frequently applied to a collection of samples from the same population, such as a set measurements performed on different days and different subjects, all stitched together into a single object. If this is the case, the underlying statistical distribution is kind of in one-to-one correspondence to the dataset, because in practice nobody really will ever perform exactly the same experiment you did on exactly the same individuals. Under this terminology, the expressions data set and population are to some extent interchangeable. While this use of language may not be very sound mathematically, it is to some extent justified by the desire to simplify presentation for the target audience
However, under the assumption of the terminology you use, you are correct, IMHO. Clearly, if a method is adequately cross-validated on sufficient samples from a given population, the probability that it would perform differently on a different sample should be quite small.
