We investigate the origin of the type III (up-bending) discs based on a sample of 1808 galaxies from Sloan Digital Sky Survey and a sub-sample of 286 galaxies with HI data from ALFALFA. We examine how the type III fraction f(III), the fraction of disc galaxies which host up-bending disc breaks, depends on other galactic properties. We confirm that fIII strongly depends on the stellar concentration of galaxies. We find that HI-rich galaxies with low spins tend to have significantly more type III disc breaks than control galaxies, which are matched in concentration and stellar mass. This trend is independent of the existence of strong bars or environment of the galaxies. This result is broadly consistent with predictions from theoretical simulations, and indicates in situ star formation fuelled by gas accretion to be an important mechanism that builds the outer discs of type III galaxies.