They also have a bad tendency to not count canibalized spending from locals: if I go to a game and spend money on food and parking, would I have spent it on food and parking doing something else that day instead.
Your doubts are absolutely correct.
This website dissects this issue in depth—sport by sport, league by league, city by city:
https://www.fieldofschemes.com/
You are talking about people flying in from other countries, hotel stays, 3 meals a day in the city. F1 also have a very exclusive club which the uber rich spend insane amount of money.
But the point is the poster was griping about the city of Austin giving the race $25 million. Even if the race brought in $100 million, which would be $231 per person, they still make money