Here's some details on how ozone effects red blood cells-
Keep in mind that ozone has the effect of oxidizing the cell walls of bacteria, viruses, etc. There's a good deal of infections that can't survive in an oxygen-rich environment, and if you give a sudden influx of it, the dieoff can overwhelm the patient. That's exactly what you see happening in lab studies that report negatively about ozone therapy.
Oxidized material is also one of the main ways the body marks tissue, minerals, matter, etc, for the immune system to act on it.
Focus on antioxidants alone is a bit naieve because of that face- the body works on a balance of oxidants and antioxidants.
I do recall an ozone therapist relating how ozone effects red blood cells, since his technique was drawing a pint of blood to insufflate (expose it to the ozone) it outside the body before feeding it back into the vein through the IV. He explained that the blood would go from the color of red wine to bright red.
How much oxygen hemoglobin can carry is a critical marker in a lot of ailments- diabetes for one, lung patients, etc.