The level structure of the very neutron rich and unbound $^9$He nucleus has been the subject of significant experimental and theoretical study. Many recent works have claimed that the two lowest energy $^9$He states exist with spins $J^pi=1/2^+$ and $J^pi=1/2^-$ and widths on the order of hundreds of keV. These findings cannot be reconciled with our contemporary understanding of nuclear structure. The present work is the first high-resolution study with low statistical uncertainty of the relevant excitation energy range in the $^8$He$+n$ system, performed via a search for the T=5/2 isobaric analog states in $^9$Li populated through $^8$He+p elastic scattering. The present data show no indication of any narrow structures. Instead, we find evidence for a broad $J^{pi}=1/2^+$ state in $^9$He located approximately 3 MeV above the neutron decay threshold.