  Spin-fluctuation-mediated unconventional superconductivity can emerge at the
border of magnetism, featuring a superconducting order parameter that changes
sign in momentum space. Detection of such a sign-change is experimentally
challenging, since most probes are not phase-sensitive. The observation of a
spin resonance mode (SRM) from inelastic neutron scattering is often seen as
strong phase-sensitive evidence for a sign-changing superconducting order
parameter, by assuming the SRM is a spin-excitonic bound state. Here, we show
that for the heavy fermion superconductor CeCoIn$_5$, its SRM defies
expectations for a spin-excitonic bound state, and is not a manifestation of
sign-changing superconductivity. Instead, the SRM in CeCoIn$_5$ likely arises
from a reduction of damping to a magnon-like mode in the superconducting state,
due to its proximity to magnetic quantum criticality. Our findings emphasize
the need for more stringent tests of whether SRMs are spin-excitonic, when
using their presence to evidence sign-changing superconductivity.
