it’s reasonable to conclude that at least one of these three is true
These often aren’t exhaustive. There’s the example of a prestigious university that only admits students who are exceptional either academically or musically. Among students at that university, academic ability is negatively correlated with musical ability, since either one is enough to be admitted, but it is rare to be exceptional in both, assuming they are uncorrelated in the general population. This does not fit into any of those three common reasons for correlation.
A similar, possibly more politically fraught example is the university that grants scholarships either on the basis of academic merit or financial need.
These often aren’t exhaustive. There’s the example of a prestigious university that only admits students who are exceptional either academically or musically. Among students at that university, academic ability is negatively correlated with musical ability, since either one is enough to be admitted, but it is rare to be exceptional in both, assuming they are uncorrelated in the general population. This does not fit into any of those three common reasons for correlation.
A similar, possibly more politically fraught example is the university that grants scholarships either on the basis of academic merit or financial need.
That’s a good scenario to think about. So maybe we can add an additional case where there’s some filtering process that’s affecting the data we see.