The problem is that it means something else in probability theory, namely the much weaker statement E(a-E(a)) E(b-E(b)) = E((a-E(a)(b-E(b))

E(a-E(a)) and E(b-E(b)) are both identically zero, so this would be more simply put (and restoring some missing parentheses) as E((a-E(a))(b-E(b))) = 0. Or after shifting the means of both variables to zero, E(ab) = 0.