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.
‘Is Personality Fixed? Personality Changes as Much as “Variable” Economic Factors and More Strongly Predicts Changes to Life Satisfaction,’ published in Social Indicators Research (doi: 10.1007/s11205-012-0006-z)
[...] small positive personality changes may lead to greater increases in happiness than earning more money, marrying, or gaining employment.
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We found that our personalities can and do change over time – something that was considered improbable until now – and that these personality changes are strongly related to changes in our wellbeing.
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Previous studies have shown that personality accounts for up to 35% of individual differences in life satisfaction, compared to just 4% for income, 4% for employment status and between 1% and 4% for marital status. However, because it was believed our personalities were fixed, policies to improve wellbeing have focused on these lower-impacting external factors.
[...]
“Fostering the conditions where personality growth occurs – such as through positive schooling, communities, and parenting - may be a more effective way of improving national wellbeing than GDP growth.”
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Personality was measured using a well-validated personality questionnaire assessing five broad dimensions which cover the breadth of a person’s personality: openness-to-experiences, conscientiousness, extroversion, agreeableness and neuroticism. The researchers then looked at the extent to which personality changed and how these changes related to life satisfaction in comparison to external factors, such as changes to income, changes to employment and changes to marital status. They found that personality changes at least as much as these external factors and predicted about twice as much of changes to life satisfaction over the study period.
Link: manchester.ac.uk/aboutus/news/display/?id=8035