It is all hidden in the QED Lagrangian:
One can answer this question in a simple way in terms of the QED Lagrangian, at the electron-field interaction part:
This tells us that interactions of the form:
are allowed. This then means that since (1) and (2) are allowed at tree level, at higher order QED the interaction (at one loop level)
is also allowed. This is because there is nothing in the fundamental QED Lagrangian, $L$, to tell us that this is not possible. Special relativity as represented by the above Lagrangian allows $E_\gamma=2m_ec^2$ as well as $2mc^2=E_\gamma.$ Quantum mechanics also allows, via the uncertainty principle, for the $e^++e^-$ pair to exist in virtual states, unless some sufficiently strong Coulomb field, or even uniform electric field, or strong gravitational field like just outside a balck hole's event horizon (Hawking radiation) separates them from each other.