Intraspecific variability (IV) has been proposed as a new track to explain species coexistence. Previous studies generally assumed, although often non-explicitely, that IV results from intrinsic differences between conspecific individuals. Under this hypothesis, IV either (i) blurred species differences, thus promoting transient or unstable coexistence, (ii) disproportionately advantaged the strongest competitor, thus hindering coexistence, or (iii) promoted coexistence. Based on a body of evidence, we here emphasize that IV does not necessarily imply inherent differences among conspecific individuals, nor species niches overlap. Conspecific individuals can also differ in their measured attributes due to differences in the micro-environment they thrive in. If this source of variation is predominant, which we suggest it is in many cases given the variation of the environment in numerous dimensions at fine scales and the observed spatial structure of IV, it implies that conspecific individuals respond more similarly to environmental variation than heterospecific individuals, thereby concentrating competition within species -- a necessary condition for species coexistence. Importantly, as the number of environmental dimensions that are typically observed and characterized in the field is generally much lower than the actual number of environmental dimensions that influence individual attributes, a great part of observed IV can often be misinterpreted as random variation across individuals while being environmentally-driven, with radically different consequences for community dynamics. We call for new studies exploring observed IV as an outcome of species-specific responses to high-dimensional environmental variations that can lead to inversions of species hierarchy in space and time promoting stable coexistence.