  We show that the universal $1/k^4$ tail in the momentum distribution of
dilute Fermi gases implies that the spectral function $A(\kk,\omega)$ must have
weight below the chemical potential for large momentum $k \gg k_F$, with
observable consequences in RF spectroscopy experiments. We find that this
incoherent spectral weight is centered about $\omega \simeq - \epsilon(\kk)$ in
a range of energies of order $v_F k$. This "bending back" in the dispersion,
while natural for superfluids, is quite surprising for normal gases. This
universal structure is present in the hard-sphere gas as well as the Fermi
liquid ground state of the highly imbalanced, attractive gas near unitarity. We
argue that, even in the BCS superfluid, this bending back at large $k$ is
dominated by interaction effects which do not reflect the pairing gap.
