  XTE J1550-564 is a black hole X-ray binary for which the dynamical
characteristics are well established, and the broadband spectral evolution of
the source has been well studied. Its orbital inclination is known to be high,
at $\sim75^{\circ}$, with the jet estimated to align well with the orbital
axis. We explore simultaneous observations made with ASCA and RXTE, covering
the $1$--$200$~keV band, during the early stages of the first outburst of XTE
J1550-564 in its hard-intermediate state, on 1998-09-23/24. We show that the
most up-to-date reflection models, applied to these data, yield an inclination
estimate much lower than found in previous studies, at $\sim40^{\circ}$,
grossly disagreeing with the dynamically estimated orbital inclination. We
discuss the possible explanations for this disagreement and its implications
for reflection models, including possible physical scenarios in which either
the inner disk is misaligned both with binary orbit and the outer jet, or
either the inner accretion flow, corona, and/or jet have vertical structure
which leads to lower inferred disk inclination through various physical means.
