In the paper 'The non-Riemannian nature of perceptual color space', the authors analyze the data of visual experiments conduced using triad of CIE L * achromatic stimuli. The statistical analysis of their results leads them to claim that the L* axis cannot be endowed with a Riemannian metric coherent with observers' responses. In this communication we provide a mathematical analysis which, in our opinion, confutes the main claim of the quoted paper. Furthermore, we raise questions on the soundness of using an achromatic perceptual coordinate to describe non-chromatic perception. We inform about an alternative in which achromaticity emerges from the very act of observing colors [2, 3].