  The dilepton production from $pC$ and $pCu$ collisions at $T_{lab}=12$ GeV is
calculated using the semi-classical BUU transport model, that includes the
off-shell propagation of vector mesons nonperturbatively and calculates the
width of the vector mesons dynamically. It is found that the collisional
broadening of the vector meson width and dropping vector meson masses lead to a
small enhancement of the dilepton yield below the $\omega$ meson mass pole in
$p Cu$ collisions compared to $p C$, which is, however, not sufficient to
explain the enhanced production of dileptons as observed in the experiment by
the KEK-PS E325 collaboration. It is argued that such in-medium effects are
expected to be small due to kinematical reasons -- the dominant part of vector
mesons radiate dileptons and decay outside the nucleus due to the finite
formation time for $\rho$ and $\omega$ mesons, which is large by Lorentz
covariance since the produced vector mesons move with high velocity relative to
the target nucleus.
