Perry T. Jones became Davis Cup Captain in 1958 and recruited Olmedo to play on the team. He represented the U.S. in Davis Cup competition in 1958 and 1959, winning in both singles and doubles – achieving 2 of the 3 points required to win the Cup. His teammates were Ham Richardson and Barry MacKay, when they won the Cup in 1958.
Though he was not a U.S. citizen, he was technically eligible to represent the U.S. in Davis Cup because he had lived in the country for at least five years and because his country of citizenship, Peru, did not have a Davis Cup team. His participation was very controversial, however. Sports columnist Arthur Dailey at the New York Times wrote, "This would seem to be the saddest day in the history of American tennis. A few more such rousing victories and the prestige of this country in tennis will sink to a new low." Olmedo himself refused to file for U.S. citizenship, said he was content to remain a Peruvian citizen, and denied he was ducking U.S. citizenship to avoid being drafted into the Army. Still, many Americans "took a dim view of the largest nation in the competition stooping to borrow a little player from Peru to win the Cup".