Lehman executives talked openly about the value of Mr. Bush's family connections in the midst of the crisis. Lehman's chief executive, Richard S. Fuld Jr., discussed the possibility of having Mr. Bush ask his brother President Bush to persuade the British prime minister to allow Lehman's emergency merger with a British bank, according to testimony from the company's bankruptcy case. Mr. Fuld never followed through, and Mr. Bush did not call the president, a spokeswoman for him said.
Friends and colleagues said Mr. Bush carefully evaluates businesses before working with them. In the case of InnoVida, an aide said, he ran a background check on the founder, a flashy, Maserati-driving businessman named Claudio Osorio. It turned up the bankruptcy of a previous company, the aide said, but nothing to suggest wrongdoing. So Mr. Bush agreed to help market his technology, a construction system that required no cement, steel or wood.
There is no evidence that board members were aware of Mr. Osorio's fraud. But Christopher Korge, an investor in the company and board member, said he recalled talking to Mr. Bush about their shared frustration with the company's delays in distributing financial information and reluctance to hold regular board meetings.
In separate interviews, a lawyer for Mr. Osorio, who pleaded guilty, and a lawyer for a group of investors argued that members of the board had exercised little meaningful oversight of the company.
"It was done lackadaisically," said David A. Nuñez, the lawyer whose clients lost millions when InnoVida collapsed. If board members "did their due diligence, really did it, they would have been able to determine this company was not financially solvent and that it was a fraud," he said.
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Mr. Korge, a major Democratic Party fund-raiser who lost millions on his investment in InnoVida, said that once he alerted Mr. Bush to major problems inside the company, the former governor acted swiftly and forcefully to investigate them. "Jeb did everything that he should have done to protect the shareholder," he said.
Most of Mr. Bush's career in business has steered clear of politics, allowing him to carefully hone a potential campaign message by delivering speeches, granting television interviews and writing a book. But not all of his corporate work is in sync with his public brand.
Mr. Bush opposed the Affordable Care Act and has called it "flawed to its core," like many of his potential rivals in the 2016 campaign. But unlike them, he has earned more than $2 million for sitting on the board a company, Tenet Health Care, that has loudly endorsed the legislation.
Tenet's chief executive, Trevor Fetter, said Mr. Bush had made no secret of his objections to the health care overhaul at company meetings. But he suggested that Mr. Bush understood the difference between "personal views and what is best for the company." Mr. Fetter predicts that in 2014, the Affordable Care Act will deliver up to $100 million in new earnings for Tenet.
—By Michael Barbaro, The New York Times, with Kitty Bennett and Andrew Ross Sorkin