  We use inelastic neutron scattering measurements to show that the energy gap
in the magnetic excitations of URu$_2$Si$_2$, induced by the Hidden Order
transition, is closed by Re substitution. The magnetic excitations remain
ungapped in compositions where the specific heat anomaly associated with Hidden
Order is no longer observed, which means that the entropy associated with
Hidden Order is tied mostly to the magnetic gapping. Further, the onset of
ferromagnetic order does not gap the excitations, reflecting the fact that Re
substitution does not dramatically affect the Kondo lattice hybridization.
