Competition can increase cortisol but it's usually a relative thing:
When you are world #200 playing against world #50 might be stressful. When you are world #2 playing world #50 is probably another day in the office. Etc
I imagine once you win your first Grand Slam in tennis the nerves improve a lot - you kind of saw that in Andy Murray who needed a couple of attempts to break through the psychological barrier of winning Wimbledon, including winning the Olympics.
I would posit that the old folk tale is more related to the fact that centuries ago, most people were hyper specialised and standardised widespread education was less of a thing.
You'll find plenty of intelligent people in all walks of life depending on how you choose to define intelligence.