  Observational follow-up of well localized short gamma-ray bursts (SGRBs) has
left $20-30\%$ of the population without a coincident host galaxy association
to deep optical and NIR limits ($\gtrsim 26$ mag). These SGRBs have been
classified as observationally hostless due to their lack of strong host
associations. It has been argued that these hostless SGRBs could be an
indication of the large distances traversed by the binary neutron star system
(due to natal kicks) between its formation and its merger (leading to a SGRB).
The distances of GRBs from their host galaxies can be indirectly probed by the
surrounding circumburst densities. We show that a lower limit on those
densities can be obtained from early afterglow lightcurves. We find that
$\lesssim16\%$ of short GRBs in our sample took place at densities
$\lesssim10^{-4}$ cm$^{-3}$. These densities represent the expected range of
values at distances greater than the host galaxy's virial radii. We find that
out of the five SGRBs in our sample that have been found to be observationally
hostless, none are consistent with having occurred beyond the virial radius of
their birth galaxies. This implies one of two scenarios. Either these
observationally hostless SGRBs occurred outside of the half-light radius of
their host galaxy, but well within the galactic halo, or in host galaxies at
moderate to high redshifts ($z\gtrsim 2$) that were missed by follow-up
observations.
