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 catalogues from the AEMULUS suite of N-body simulations, which span a range of omega CDM cosmological models. We focus on reconstruction of the primordial BAO and locating the BAO. For the range of omega CDM cosmologies covered by the AEMULUS suite, we find no evidence for systematic errors in the measured BAO shift parameters alpha(parallel to) and alpha(perpendicular to) to < 0.1%. However, the measured errors sigma(alpha parallel to) and sigma(alpha perpendicular to) 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.