We revisit the uncertainty in baryon acoustic oscillation (BAO) forecasts and data analyses. In particular, we study how much the uncertainties on both the measured mean dilation scale and the associated error bar are affected by the non-Gaussianity of the non-linear density field. We examine two possible impacts of non-Gaussian analysis. (1) We derive the distance estimators from Gaussian theory, but use 1000 N-body simulations to measure the actual errors, and compare this to the Gaussian prediction. (2) We compute new optimal estimators, which requires the inverse of the non-Gaussian covariance matrix of the matter power spectrum. Obtaining an accurate and precise inversion is challenging, and we opted for a noise reduction technique applied on the covariance matrices. By measuring the bootstrap error on the inverted matrix, this work quantifies for the first time the significance of the non-Gaussian error corrections on the BAO dilation scale. We find that the variance (error squared) on distance measurements can deviate by up to 12 per cent between both estimators, an effect that requires a large number of simulations to be resolved. We next apply a reconstruction algorithm to recover some of the BAO signal that had been smeared by non-linear evolution, and we rerun the analysis. We find that after reconstruction, the rms error on the distance measurement improves by a factor of ∼1.7 at low redshift (consistent with previous results), and the variance (σ2) shows a change of up to 18 per cent between optimal and sub-optimal cases (note, however, that these discrepancies may depend in detail on the procedure used to isolate the BAO signal). We finally discuss the impact of this work on current data analyses.