In [EH89, Theorem 1] Ekeland-Hofer prove that for a centrally symmetric,
restricted contact type hypersurface in R^{2n} and for any global, centrally
symmetric Hamiltonian perturbation there exists a leaf-wise intersection point.
In this note we show that if we replace restricted contact type by star-shaped
there exists infinitely many leaf-wise intersection points or a leaf-wise
intersection point on a closed characteristic.