There's also a related problem in that population substructures can give you multiple negatively correlated associations stacked beside each other in a positively correlated way (think of it like several diagonal lines going downwards to the right, parallel to each other), giving an 'ecological fallacy' when you switch between levels of analysis.

(A real-world case of this is religiosity and health. Internationally, countries which are less religious tend to be healthier, but often within first world countries, religion confers a survival benefit.)