A U-statistic is the Rao–Blackwellisation of any unbiased kernel estimator

Let $S=S(X_1,X_2,\dots,X_n)$ be an unbiased estimator of the parametric functional $\theta(F)$ based on a random sample $X_1,X_2,\dots,X_n$ from F. Suppose U is the U-statistic corresponding to S. Then, which of the following statements is true?