The D and F scales have statistically independent underlying factor structures.

Evidence

When Kerlinger and Rokeach examined their ten first-order factors, five of them were basically loaded with D Scale items, and three were basically loaded with F Scale items. The correlations among the ten obliquely rotated factors were then themselves factor analyzed, and the three resulting second-order factors were graphically rotated into an orthogonal structure. Four of the five first-order “‘D Factors” had their highest loadings on the first second-order factor, while the three first-order “F Factors” had their highest loadings on either the second or the third second-order factors. — Bob Altemeyer, The Authoritarian Specter, 2596