We re-examine the observational evidence for large-scale (4 Mpc) galactic conformity in the local Universe, as presented in Kauffmann et al. (2013). We show that a number of methodological features of their analysis act to produce a misleadingly high amplitude of the conformity signal. These include a weighting in favour of central galaxies in very high-density regions, the likely misclassification of satellite galaxies as centrals in the same high-density regions, and the use of medians to characterize bimodal distributions. We show that the large-scale conformity signal in Kauffmann et al. clearly originates from a very small number of central galaxies in the vicinity of just a few very massive clusters, whose effect is strongly amplified by the methodological issues that we have identified. Some of these 'centrals' are likely misclassified satellites, but some may be genuine centrals showing a real conformity effect. Regardless, this analysis suggests that conformity on 4 Mpc scales is best viewed as a relatively short-range effect (at the virial radius) associated with these very large neighbouring haloes, rather than a very long-range effect (at tens of virial radii) associated with the relatively low-mass haloes that host the nominal central galaxies in the analysis. A mock catalogue constructed from a recent semi-analytic model shows very similar conformity effects to the data when analysed in the same way, suggesting that there is no need to introduce new physical processes to explain galactic conformity on 4 Mpc scales.