It wasn't John Wooden, it was sports journalist and commentator Heywood Hale
("Woodie") Broun who said it.
<http://slick.org/deathwatch/mailarchive/msg00358.html> Broun, who had a
distinctive brush moustache and wore loud plaid jackets when he reported on
CBS, pronounced his last name "broon".
He and his generation are probably why there's a widely-held concept of the
SOTG. Modern sports journalists, with a few exceptions, don't have a clue.
His actual words, before James A. Michener published the above quotation in
his 1976 book, Sports in America, may have been "Sports doesn't build
character; It reveals character." Michener supposedly said later, "Sports
develops not character, but characters."