Its not Debusschere. he had a brief stint for the Chisox and less than a cup of coffee for the Indians, all in the early '60s. Perhaps my mistaken memory of the Tigers resulted from the fact that Double D was traded from the Detroit Pistons to the Knicks (for center Walt Bellamy).
I can only come up with two other players who you might be thinking of. One was a fantastic college basketball player (Player of the Year as a Senior) who played briefly in the NBA. He then went on to have a near HOF baseball career. This player did not win a basketball championship in either college or the pros, but he was an integral part of two World Series champions (different teams, same opponent). The second player was on the LOSING end of both one NBA championship and two World Series. He was a moderately talented but never outstanding player in either sport.