This is a question about the rhetoric of describing analysis done using a public data set or any other pre-existing data set.
Here is the hypothetical situation: A researcher reports that they have a hypothesis. To test this, they take a sample, n, of individuals that meets study criteria from a database of N participants. They run a single, a priori, test of this hypothesis on the sample, and report that the hypothesized group difference, or correlation, or whatever, is greater than 0, p<.05.
Is this exploratory or is it a fine example of hypothesis testing?
Because any single reported analysis of an existing data set might be one of many interrogations, any such report should be framed as exploratory rather than hypothesis testing. In other words, presenting an analysis of an existing data set using the rhetoric of a single sample hypothesis test seems to be misleading the reader to over-interpret the results.
However, I can also see an argument being made for the researcher being given the benefit of the doubt as is similarly the case in all non-pre-registered studies. In other words, can we assume that the researcher did just test this one hypothesis on this single subset of the existing database?