What exactly is the "oxygen reduction reaction"?
According to your cited paper the reaction they care most about is $$\ce{O2 + 4H+ + 4e- -&gt; 2H2O}$$ as you are suggesting. This should also be the total reaction and the most interesting one for applications, e.g. in fuel cells.

There are various suggestions for the mechanistics of the Oxygen Reduction Reaction. A quite recent review was published by Nagappan Ramaswamy and Sanjeev Mukerjee. A very early general scheme can be found at electronicstructure.wikidot.com, where they cited Halina S. Wroblowa et.al..