  The narrow, neutral Fe K{\alpha} fluorescence emission line in X-ray binaries
(XRBs) is a powerful probe of the geometry, kinematics and Fe abundance of
matter around the accretion flow. In a recent study it has been claimed, using
$Chandra$ High-Energy Transmission Grating (HETG) spectra for a sample of XRBs,
that the circumnuclear material is consistent with a solar-abundance, uniform,
spherical distribution. It was also claimed that the Fe K{\alpha} line was
unresolved in all cases by the HETG. However, these conclusions were based on
ad hoc models that did not attempt to relate the global column density to the
Fe K{\alpha} line emission. We revisit the sample and test a self-consistent
model of a uniform, spherical X-ray reprocessor against HETG spectra from 56
observations of 14 Galactic XRBs. We find that the model is ruled out in 13/14
sources because a variable Fe abundance is required. In 2 sources a spherical
distribution is viable but with non-solar Fe abundance. We also applied a
solar-abundance Compton-thick reflection model, which can account for the
spectra that are inconsistent with a spherical model, but spectra with a
broader bandpass are required to better constrain model parameters. We also
robustly measured the velocity width of the Fe K{\alpha} line and found full
width half maximum values up to ~5000 km s$^{-1}$. Only in some spectra was the
Fe K{\alpha} line unresolved by the HETG.
