Recently, [Herrada, M. A. and Eggers, J. G., Proc. Natl. Acad. Sci. U.S.A. 120, e2216830120 (2023)] reported predictions for the onset of the path instability of an air bubble rising in water and put forward a physical scenario to explain this intriguing phenomenon. In this Brief Report, we review a series of previously established results, some of which were overlooked or misinterpreted by the authors. We show that this set of findings provides an accurate prediction and a consistent explanation of the phenomenon that invalidates the suggested scenario. The instability mechanism actually at play results from the hydrodynamic fluid-body coupling made possible by the unconstrained motion of the bubble which behaves essentially, in the relevant size range, as a rigid, nearly spheroidal body on the surface of which water slips freely.