There was a rather compelling pathway proposed years ago: skeletal muscle activation leads to the secretion of a protein in the blood called Irisin. This protein then crosses the blood-brain barrier and upregulates brain-derived neurotrophic factor.
Yet there are always examples of extraordinary minds of people who either despise physical exercise it are even wheelchair-bound. Steven Hawkins comes to mind. Maybe those are just exceptions.
I see no reason to think that people don't have different cognitive baselines. It's not difficult to imagine two people having such different cognitive baselines that even if exercise improves the cognitive ability of one, it will still be lower than the cognitive ability of the other without exercise.
I never did turn into a super genius after a run. But I can focus for a few hours and if it was an easy run or even a hard strength training session, it is a productive few hours :)
