Are methods of p-value adjustment only necessary when a universal/overall hypothesis is the target of inference? I am trying to understand more clearly in which cases an adjustment of p-values is necessary. At the moment my reasoning about this can be summarized as follows:
Benjamini and Hochberg (1995) list three problems/scenarios where adjustment of the type I error is called for:

*

*multiple outcomes ("multiple end points problem"),

*multiple comparisons ("multiple-subgroups problem") and

*"screening problem" (e.g. screenin of multiple predictors).

Some, for instance Perneger (1998) have argued that such adjustment is necessary only in cases in which one wants make an inference about a "universal hypothesis" from multiple tests.
To me, all three of the above scenarios can be understood as such a case: In scenario 1) the overall (=univeral) hypothesis is that the treatment has an effect (on at least one of the outcomes). In scenario 2) the overall hypothesis is that there are (any) differences between conditions. In scenario 3) the overall hypothesis might be that any of the predictors affects the outcome (although that logic is less clear to me in this case).
So does that mean that drawing an inference about such an overall hypothesis (using several seperate tests) is the main/real/only reason for using p-value adjustment methods?
And does that mean that if I strictly avoid inferences about an overall hypotheses of any kind (directly/implicitly or otherwise), then there is no reason to use such adjustment methods?
Or am I misunderstanding something here (and if so, what)?

I think you are essentially correct.  As you can see, the common thread in the three scenarios you describe is that there are multiple comparisons to make some overall inference.  When you perform hypothesis testing with multiple comparisons, you generally end up looking at the test with the lowest p-value, because this is the one with the greatest evidence for a deviation from the null hypothesis.  This means that you are effectively "optimising" over multiple tests.  The null distribution of the lowest p-value is not uniformly distributed, and its distribution tends to put heavy density on lower values.  Adjustment is then required to get an "overall p-value" that accounts for this and moves the null distribution back to a uniform distribution (hopefully).
