I remember one of my physics professors at uni explaining this theory and for some reason, I had this weird anxiety at the thought. A lonely electron doing all the work of every electron in the universe. Semifun fact, Feynman used the electron traveling back in time analogy to help teach the principles of QED.
The theory also has some merit at least in the boundaries of QED, it's impossible to draw a QED Feynman diagram where the arrows representing positron/electrons just stop, each one must eventually reach the other end of the diagram.
It doesn't quite work as you move beyond that, you get stuff like neutrons decaying into protons and electrons (and some neutrinos somewhere). Unless of course you take seriously consider Wheeler's suggestion that the positrons might be hiding in the protons.
Given that gravity has been observed to work on antimatter the same way as it does on normal matter, doesn't that refute this? or is there another aspect of symmetry that keeps it consistent?