Later, when introduced from the audience, Stevenson stood and waved but the Cuban line is drawn at communication. On alien territory, their economy almost wrecked by trade sanctions imposed as a result of electoral pressure on the Clinton administration, running the risk of further defections, they are seen but not heard.
After winning their bouts on day one of the Olympic boxing tournament, the bantamweight Arnaldo Mesa and the welterweight, Juan Hernandez proved to be as tight-lipped as team officials who ignore interrogators.
The American attorney John Hornewer, who represents Lennox Lewis, has their confidence but can do nothing to find a way through the barrier of silence. Last week, Hornewer thought he had succeeded in setting up an interview with the head of Cuba's boxing delegation for a leading New York sports columnist. "I got them together,'' he said, "but none of the questions were answered.''
Fascination founded on the conflict of ideology that flexed United States muscle in the Olympics until communism collapsed in eastern Europe, is understandable. Castro's Cuba stands alone, isolated in the shadow of its glowering neighbour, and yet still capable of quite remarkable athletic achievement.
If Cuba are no longer the force that took seven of the 12 boxing gold medals in Barcelona they are nevertheless still equipped to strike a blow at American pride.
However, even if the US manage to reverse the fortunes of four years ago when their only gold medal was won by Oscar de la Hoya who has since established himself as an outstanding professional champion, it is unlikely to make much impact on American television.
All right, it seems for the NBC network to exploit the greatness of a sadly stricken Muhammad Ali at Friday's opening ceremony - the sight of his trembling hands when applying a torch to the Olympic flame made me feel uneasy - but not to celebrate the sport that made him the greatest sports figure in history.
Opting not to give boxing prime time coverage, NBC has relegated it to late night viewing. "When we put out boxing we lose up to 75 per cent of the female audience,'' Dick Ebersol, who is president of NBC sports, said.
At the 1976 Olympics in Montreal no US competitor gained greater popularity than Sugar Ray Leonard but times have changed. The burning question today is whether NBC and the International Olympic Committee would prefer to banish boxing.
Controversial decisions - the present International Boxing Federation super-middleweight champion, Roy Jones, who is considered to be the best fighter, pound for pound, at work in the professional ring was blatantly robbed of a gold medal in 1988 - have served to put the Olympic boxing tournament at risk.
Gone is the Olympic glamour that marked the emergence of such notable figures as Ali, George Foreman, Joe Frazier, Leonard and Evander Holyfield. A United States team press conference last week was held in a ramshackle arena. "Any sport made up of kids from inner-city areas has a problem getting the public's attention,'' the US coach, Al Mitchell said.
Ed Schuyler, of the Associated Press, who had covered 1,613 Olympic bouts before Atlanta, believes that the NBC network is only interested in the negative aspects of boxing. "If there was a tragedy in the ring, a political controversy, a riot in the crowd, you would not be able to move for cameras,'' he said.
Another reason for NBC's reluctance to provide boxing with prime time coverage may be scandals involving members of the US team. The super-heavyweight Clay-Bey has been accused of sexual assault in his home town, Hartford. The strongly fancied light-heavyweight Antonio Tarver is a reformed crack addict. The heavyweight Nate Jones served 20 months for armed robbery. The father of featherweight Floyd Mayweather is serving time for cocaine trafficking.
However, none of this appears to have affected local enthusiasm for the efforts of US boxers. With two home competitors, bantamweight Zahir Raheem and welterweight Fernando Vargas, on Saturday's card there was a full house at the Alexander Memorial Coliseum at Georgia Tech. "I don't think many people are put off by the bad things that have been said about boxing,'' Mitchell added. "More should be said about the positive things these kids are doing now, the role boxing has is turning their lives around.''
That Saturday's sessions passed without incident - "a screw-up in scoring'' - surprised veteran observers, but give it time. At least the five judges appointed to each bout appear to be punching the buttons more frequently than in Barcelona where some fighters were the victims of ludicrously distorted judgements.
The best way of course is to follow Stevenson's example. In winning three golds he repeatedly knocked opponents silly.