As it sought to recruit well-heeled investors, an untested and unprofitable Miami company named InnoVida brought aboard a trusted Florida figure in 2007: Jeb Bush, the former governor and the brother of a sitting president. For potential stockholders, the imprimatur of Mr. Bush, who joined InnoVida as a paid consultant and a member of the board of directors, conferred credibility on the young start-up. That credibility did not last long. It turned out that the leaders of InnoVida, a manufacturer of inexpensive building materials, had faked documents, lied about the health of the business and misappropriated $40 million in company...