The genetic explanation doesn't even require a correlation between the traits of people who pair up. Suppose your grandparents genetic "quality" is statistical

The genetic explanation doesn't even require a correlation between the traits of people who pair up. Suppose your grandparents genetic "quality" is statistically independent, so you have four quantities g1, g2, g3, g4. Your parents quality is approximately (g1 + g2) / 2 and (g3 + g4) / 2 and yours is (g1 + g2 + g3 + g4) / 4. Now if we assume that income is a noisy measure of your "g" then it will follow that your income is correlated with your grandparents' even after accounting for your parents' income.