We reveal the existence of a large in-plane heavy-hole g factor in symmetric self-Assembled (001) (In,Ga)As/GaAs quantum dots due to the warping of valence-band states. This warping dominates over the well-established mechanism associated with a reduced symmetry of the quantum dots and the corresponding mixing of heavy-hole and light-hole states. The effect of band warping is manifested in a unique angular dependence of the trion photon echo signal on the direction of the external magnetic field with respect to the sample axes. It results in a uniform magnetic-field-induced optical anisotropy for the entire quantum dot ensemble which is a prerequisite for the realization of spin quantum memories and spin-photon entanglement in the ensemble.