We present a comprehensive investigation of the polarization properties of non-polar a-plane InGaN quantum dots (QDs) and their origin with statistically significant experimental data and rigorous k.p modelling. The unbiased selection and study of 180 individual QDs allow us to compute an average polarization degree of 0.90, with a standard deviation of only 0.08. When coupled with theoretical insights, we show that a-plane InGaN QDs are highly insensitive to size differences, shape anisotropies, and indium content fluctuations. Furthermore, 91% of the studied QDs exhibit a polarization axis along the crystal [1-100] axis, with the other 9% polarized orthogonal to this direction. When coupled with their ability to emit single-photons, a-plane QDs are good candidates for the generation of linearly polarized single-photons, a feature attractive for quantum cryptography protocols.