I understand it, you don't. And it's not fine. Now pay attention:Nope, looks fine to me. You have quoted a wordy verbal description of the well-tested QED Lagrangian, cited later in the paper, which is the part that makes the testable predictions. If you have a problem with a QED, you have to have a problem with that Lagrangian. Which you don't. Because you don't understand it.
"Virtual electron-positron pairs, can in principle, be polarised by an external electromagnetic field, thus introducing non-linearities into Maxwell’s equations, which break the familiar principle of superposition of electromagnetic waves in vacuum. Photons from multiple, vacuum-polarising sources, can then become coupled on the common point of interaction of the polarised virtual pairs".
It's gamma-gamma pair production remember? But it's saying a photon interacts with a virtual electron-positron pair. It's saying pair production occurs because pair production has already occurred. It's a tautology. It's wrong. A photon does not spend its sad little life magically morphing into an electron-positron pair that magically manage to morph back into a single photon, which nevertheless manages to keep on going at c. QED does not model the photon-photon interaction.
Right, I'm off to bed. You've got until tomorrow to try and save some face.