Based on a tight-binding study of the electronic spin structure in self-assembled InGaAs/GaAs quantum dots, we propose a theory to explain why the electron g factor in these artificial atoms is insensitive to the variation of the structural dimensions and chemical composition profile and also present a microscopic picture to understand the isotropic behavior of the lateral electron g factor. The former provides an important justification for the recent experimental measurement of electron g factors in an ensemble of quantum dots, while the latter overrides the common knowledge that the shape anisotropy of quantum dots has an important effect on the in-plane electron g-factor anisotropy.