Supernumerary rainbows are indeed caused by the interference of light waves following internal reflection within raindrops, a phenomenon explained by wave optics and Airy theory.
The retrieved literature consistently supports the wave-optical and interference-based mechanism of supernumerary rainbows. Paper 3 and 11 detail how interference and wave optics (as opposed to pure geometric optics) account for supernumerary bows, and Paper 8 discusses the interference phenomena of internal rays in spherical particles. No papers contradict the claim.