  Recently, the contribution of positronium bound states to the electron
anomalous magnetic moment was computed in Refs.[1,2]. It was argued there that
this O(alpha^5) contribution is missed if electron g-2 is calculated within
conventional perturbative QED and, as such, it must be added to the
perturbative five-loop result. We show that this conclusion is flawed and that
no additional contributions to g-2 are generated in QED beyond the perturbation
theory.
