Let (G, L, tau) be an affine symmetric space with G a simple Lie group, tau an involutive automorphism of G and L an open subgroup of the tau -fixed point group G(tau). It is proved here that the existence of a proper semigroup S subset of G with intS not equal 0 and L subset of S implies that (G, L, tau) is of Hermitian type, as conjectured by Hilgert and Neeb [4]. When S exists, it turns out that it leaves invariant an open L-orbit in a minimal flag manifold of G. A byproduct of our approach is an alternate proof of the maximality of the compression semigroup of an open orbit (see Hilgert and Neeb [3]).3213587600