The evolution of the magnetic moment as a function of the applied magnetic field for a superconducting material is usually described by the so-called Bean model. We show here that this model fails to explain the magnetic response of conventional type-II superconductor films to a field applied perpendicular to the film plane when their thickness is below 100 nm. More precisely, after zero-field cooling below the critical temperature, a positive moment forms in ascending field and an increasing negative moment develops when sweeping the field back to zero. We infer that such an inverted loop behavior in the case of low-thickness films originates from a combination of low pinning, large penetration depth, and large edge demagnetization field. From relaxation experiments, we demonstrate that the magnetic states along the inverted moment versus field loop are stable equilibrium states. Our findings provide some hints to further understand the high-field paramagnetic Meissner effect reported in thin films and prove that field cooling is not required to produce a paramagnetic-like response.