The Magellanic Clouds (MCs) are the most massive gas-bearing systems falling into the Galaxy at the present epoch. They show clear signs of interaction, manifested in particular by the Magellanic Stream, a spectacular gaseous wake that trails from the MCs extending more than 150° across the sky. Ahead of the MCs is the `Leading Arm' usually interpreted as the tidal counterpart of the Magellanic Stream, an assumption we now call into question. We revisit the formation of these gaseous structures in a first-infall scenario, including for the first time a Galactic model with a weakly magnetized, spinning hot corona. In agreement with previous studies, we recover the location and the extension of the Stream on the sky. In contrast, we find that the formation of the Leading Arm - that is otherwise present in models without a corona - is inhibited by the hydrodynamic interaction with the hot component. These results hold with or without coronal rotation or a weak, ambient magnetic field. Since the existence of the hot corona is well established, we are led to two possible interpretations: (i) the Leading Arm survives because the coronal density beyond 20 kpc is a factor ≳10 lower than required by conventional spheroidal coronal X-ray models, in line with recent claims of rapid coronal rotation; or (ii) the `Leading Arm' is cool gas trailing from a frontrunner, a satellite moving ahead of the MCs, consistent with its higher metallicity compared to the trailing stream. Both scenarios raise issues that we discuss.