"Everyone spoke of a duel between east and west, and that's what it was," Dresden-born grand master Schmid remembers of the match played in Reykjavik, Iceland. "I was accepted by both players," he said.
The West German saw the delayed finally start on July 11. "I play chess, so I can put myself in the players' place," said Schmid, now an 84-year-old publisher living in Bamberg, where he says Fischer visited him twice.
The 29-year-old challenger from the US, took on the Russian World Champion Spassky, six years his senior. But there were protracted and increasingly ill-tempered negotiations to get through first.
"It was possible after all to bring such two very different characters together," said Schmid, who had already refereed the semi-final between Fischer and Armenian Tigran Petrosian a year earlier.
Fischer's eccentricities did not help the talks. The Chicago-born genius made several demands from the US in the run-up to the match, missed the opening ceremony, and only flew to Reykjavik on July 4, after he secured a promise that the players receive a share of the TV and box office proceeds. The chessboard also had to be re-made at his insistence.
The result was a two-day postponement of the first game, which Spassky only agreed to after Fischer had written a letter of apology.
"The delay was lucky for me," says Schmid. "It meant I could fly home. My son had fallen off his bicycle and was lying in hospital."
The first game, played before 2,500 spectators, was ended after a blunder from Fischer on the 29th move. "I played like a fool," he said afterwards.
The American then forfeited the second game by refusing to appear after a dispute over the TV cameras and lighting in the venue.
Schmid's decisive moment then came before the third game - played in a smaller room - when he prevented an increasingly annoyed Spassky from walking off after Fischer went round inspecting all the TV cameras.
"Both players were taller than me," he recalls. "I grabbed them by the shoulders, pushed them down, and demanded: 'Play now!' " Spassky moved his pawn and the game began.
Fischer won a brilliant game, and dominated the rest of the championship, finally winning 12.5 to 8.5 after 21 games. On September 1, he was crowned the first official US world champion since Wilhelm Steinitz in the 19th century.
A re-match was scheduled in Belgrade, Yugoslavia, in 1992, in violation of a UN embargo. Fischer demanded - and got - $3.35 million in prize money for beating Spassky in the "Revenge Match of the 20th Century." Once again Schmid was the referee.
"Fischer was not really evil," he concludes. "He was out of the ordinary, strange, different, and a real chess genius."