  Measurements of the mean free path of Lyman-continuum photons in the
intergalactic medium during the epoch of reionization can help constrain the
nature of the sources as well as sinks of hydrogen-ionizing radiation. A recent
approach to this measurement has been to utilize composite spectra of multiple
quasars at $z\sim 6$, and infer the mean free path after correcting the spectra
for the presence of quasar proximity zones. This has revealed not only a steep
drop in the mean free path from $z=5$ to $z=6$, but also potentially a mild
tension with reionization simulations. We critically examine such direct
measurements of the mean free path for biases due to quasar environment,
incomplete reionization, and quasar proximity zones. Using cosmological
radiative transfer simulations of reionization combined with one-dimensional
radiative transfer calculations of quasar proximity zones, we find that the
bias in the mean free path due to overdensities around quasars is minimal at
$z\sim 6$. Patchiness of reionization at this redshift also does not affect the
measurements significantly. Fitting our model to the data results in a mean
free path of $\lambda_{\mathrm{mfp}}=1.49^{+0.47}_{-0.52}$~pMpc at $z=6$, which
is consistent with the recent measurements in the literature, indicating
robustness with respect to the modelling of quasar proximity zones. We also
compare various ways in which the mean free path has been defined in
simulations before the end of reionization. Overall, our finding is that recent
measurements of the mean free path appear to be robust relative to several
sources of potential bias.
