"You obviously don't know anything about the Internal Combustion Engine."
Please understand that the human body is 1000x more complex than the internal combustion engine and scientists and researchers are still many years away (if at all) from creating a system that mimics the mechanisms involved with human muscle contraction/force production.
"I never said I knew anything about whatever it was you decided to spew"
And yet you feel qualified to criticize a model for performance and fatigue? Too much kool-aid this morning?
To the original OP...you did ask for physiological benefits but one can't completley disconnect the psychological from the physiological.
From a strictly physiological view (metabolism/muscle contractions operating in a vacuum), if your work load is the same your adaptations to said work load will be the same. I know that isn't what you want to hear but since you've dismissed the idea of a joint psychological/physiological process...that's what you're left with.
If you train alone you most likely will not be able to achieve the same work loads that you would be able to if you trained with someone else. Thus, your physiological adaptations will be less.