McChrystal sent an e-mail to warn that the Tillman investigation might reveal he was killed by friendly fire.
McChrystal refused to answer Woodruff's questions about Tillman during an interview in Afghanistan in July.
Rumsfeld refused to be interviewed.
In writing the book, Krakauer denied having political motives or a dislike for the Bush administration.
"I was dismayed by the invasion of Iraq as Pat was," he said. "When I started out to write this book, you know I had no intention about writing about politics. I was fascinated with Pat Tillman. And I just became increasingly outraged when I learned from talking to his platoon mates and looking through the investigations, what the government -- the Army had done to him. So my anger comes from someplace very deep and very real."
Tillman had made it clear that he did not want the military to have any direct involvement with his funeral. He made his wishes known in a standard Army deployment form that he had to fill out before he left for Iraq.
"When Pat was alive, the Army tried to make him into their poster boy for the global war on terror," Krakauer said. "And he resisted. And after he died, when he wasn't around to object, they really turned him into this -- their poster boy. And they didn't want to come across as having shot their poster boy. So they had to suppress that. They didn't want to add bad news. Instead, they very cleverly turned Pat into diversion. They turned him into a hero and the country was diverted from the bad stuff in Iraq to Pat Tillman, hero. And it worked for a while."
Krakauer said Tillman would be furious to find out what his family has suffered at the hands of the Army and the government.
"He would want to come down and wring someone's neck for sure," he said.