In our hierarchical structure-formation paradigm, the observed morphological evolution of massive galaxies -- from rotationally-supported discs to dispersion-dominated spheroids -- is largely explained via galaxy merging. However, since mergers are likely to destroy discs, and the most massive galaxies have the richest merger histories, it is surprising that any discs exist at all at the highest stellar masses. Recent theoretical work by our group has used a cosmological, hydrodynamical simulation to suggest that extremely massive (M* > 10^11.4 MSun) discs form primarily via minor mergers between spheroids and gas-rich satellites, which create new rotational stellar components and leave discs as remnants. Here, we use UV-optical and HI data of massive galaxies, from the SDSS, GALEX, DECaLS and ALFALFA surveys, to test these theoretical predictions. Observed massive discs account for ~13% of massive galaxies, in good agreement with theory (~11%). ~64% of the observed massive discs exhibit tidal features, which are likely to indicate recent minor mergers, in the deep DECaLS images (compared to ~60% in their simulated counterparts). The incidence of these features is at least four times higher than in low-mass discs, suggesting that, as predicted, minor mergers play a significant (and outsized) role in the formation of these systems. The empirical star-formation rates agree well with theoretical predictions and, for a small galaxy sample with HI detections, the HI masses and fractions are consistent with the range predicted by the simulation. The good agreement between theory and observations indicates that extremely massive discs are indeed remnants of recent minor mergers between spheroids and gas-rich satellites.