  Standard analysis pipelines for measurements of Baryon Acoustic Oscillations
(BAO) in galaxy surveys make use of a fiducial cosmological model to guide the
data compression required to transform from observed redshifts and angles to
the measured angular and radial BAO peak positions. In order to remove any
dependence on the fiducial cosmology from the results, all models compared to
the data should mimic the compression and its dependence on the fiducial model.
In practice, approximations are made when testing models: (1) There is assumed
to be no residual dependence on the fiducial cosmology after reconstruction,
(2) differences in the distance--redshift relationship are assumed to match a
linear scaling, and (3) differences in clustering between true and fiducial
models are assumed to be removed by the free parameters used to null the
non-BAO signal. We test these approximations using the current standard
measurement procedure with a set of halo catalogs from the {\sc Aemulus} suite
of $N$-body simulations, which span a range of $w\mathrm{CDM}$ cosmological
models. We focus on reconstruction of the primordial BAO and locating the BAO.
For the range of $w\mathrm{CDM}$ cosmologies covered by the {\sc Aemulus}
suite, we find no evidence for systematic errors in the measured BAO shift
parameters $\alpha_{\parallel}$ and $\alpha_{\bot}$ to $< 0.1\%$. However, the
measured errors $\sigma_{\alpha_{\parallel}}$ and $\sigma_{\alpha_{\bot}}$ show
a notable absolute increase by up to $+0.001$ and $+0.002$ respectively in the
case that the fiducial cosmology does not match the truth. These effects on the
inferred BAO scale will be important given the precision of measurements
expected from future surveys including DESI, Euclid, and WFIRST.
