Hein Donner was the first Dutch professional chess grandmaster (even Euwe was an amateur in the literal sense of the word), and he was way older than Fischer. Donner even took care of Fischer when he was 14/15 and alone on tournaments. So you are right, that statement cannot be correct.
Fischer was the first professional player? (by My great predecessors)

Emanuel Lasker was the first master who seriously attempted, -- by demanding large fees, -- to improve the chess master's financial position.
Later on Bobby Fischer repeated this with his unusual claims.
In the Communist time more masters had other occupations, Polugayevsky was a railway engineer and Spassky a journalist ; in practice they were full-time professional players.
The basic question : " ... a professional player ... " means in my opinion a player who can support himself and his family solely by chess,
On my great predecessor, Kasparov (or whoever the real author is) stated that Fischer was the first professional player. I don't understand what he mean with this affermation. Maybe his dedication and passion for the game made him a real professional, completely devoted to chess. But there were also other players like him, completely devoted to chess, like Alekhine, Rubinstein or Tal. Someone could explain that to me?