  In their 2006 paper setting the current limit on \mumemconv\ conversion
search on a gold target \cite{sindrum_ii:Bertl2006}, the SINDRUM-II
collaboration published, along with the electron momentum distribution, the
momentum distribution of reconstructed positrons. Near the positron spectrum
endpoint, there is a statistically significant excess of observed events over
the expected background. We estimate that in the region 88 MeV/c < p < 95 MeV/c
there are 13 events with an expected background of about 1-1.5 event, which has
not been discussed by the authors. Those 13 events form a bump with a width
consistent with the experimental resolution, making one think of a $\mu^-
\rightarrow e^+$ conversion signal. However, the reconstructed position of the
bump is about 1 MeV/c, or $\sim\ 4\sigma_p$, lower than the expected $\mu^- Au
\rightarrow e^+ Ir $ signal, which strongly discourages the exotic
interpretation. The excess, however, could be due to an exclusive dipole
radiative muon capture (RMC) transition $^{197}Au(GS) ~\rightarrow~
^{197}Pt(GS)$ with the branching fraction of about $2\cdot 10^{-4}$. Such a
transition would not be resolved by the existing RMC measurements. We conclude
that the exclusive RMC transitions could significantly modify the positron
spectrum near the kinematic endpoint, to fully exploit the physics potential of
the upcoming experiments such as Mu2e and COMET, a better theoretical
understanding of the RMC spectrum on nuclei is needed. A high-resolution
measurement of the RMC photon spectra has to be carried out. Without that, the
sensitivity of the searches for $\mu^- \rightarrow e^+$ and $\mu^- \rightarrow
e^-$ might be severely limited by unknown probabilities of RMC transitions to
the exclusive low-lying states of the daughter nuclei.
