Group-III-nitride semiconductors have shown enormous potential as light sources for full-colour displays, optical storage and solid-state lighting. Remarkably, InGaN blue- and green-light-emitting diodes (LEDs) emit brilliant light although the threading dislocation density generated due to lattice mismatch is six orders of magnitude higher than that in conventional LEDs. Here we explain why In-containing (Al,In,Ga)N bulk films exhibit a defect-insensitive emission probability. From the extremely short positron diffusion lengths (<4 nm) and short radiative lifetimes of excitonic emissions, we conclude that localizing valence states associated with atomic condensates of In-N preferentially capture holes, which have a positive charge similar to positrons. The holes form localized excitons to emit the light, although some of the excitons recombine at non-radiative centres. The enterprising use of atomically inhomogeneous crystals is proposed for future innovation in light emitters even when using defective crystals.