We explain why the so-called "trion line'' in the absorption spectrum of doped wells, cannot be due to a set of 3-body trions but has to come from a singular many-body object, intrinsically wide in energy: the photocreated virtual exciton dressed by Coulomb and Pauli interactions with the well carriers. This understanding is experimentally supported by the highly asymmetrical shape of the circular dichroism spectra obtained with a spin-polarized Fermi sea: their sharp edge on the low-energy side and significant tail at high energy are well explained by this many-body object, while they completely rule out a set of trions, either free or bound.