COPENHAGEN — For a world too often resentful in recent years of American arrogance, of American boastfulness, of self-styled American superiority, here were some two dozen U.S. Olympic and Paralympic athletes carrying a message of humility and engagement, tolerance and respect.

This was no act.

This was genuine — a reflection of the powerful role that sport has played in shaping their lives and of the import of the Olympic and Paralympic movements in animating the dreams that many of them saw through to gold, silver and bronze.

“I always say that sport changed my life,” Bryan Clay, the 2008 Beijing decathlon champion, said. “It put me on a path that made me a better person.”

“Sport brings people together like nothing I have ever seen,” said David Robinson, the basketball Hall of Famer. “There are no political barriers, no cultural barriers. Nothing.”