"And bottling beer, you are leaving that 1 inch of head space which contains oxygen. It is surely the priming sugar that restarts fermentation a bit, which creates CO2 and gets rid of the O2 correct? If so, wouldn't these do that also?"
I've read it's good to set the cap on the bottle for about 10 minutes before crimping to drive off the o2. The co2 doesn't get rid of the o2 if the cap is tight though.