The suspect in the Fort Hood shootings, Maj. Nidal Malik Hasan, had previously worked at Walter Reed Army Medical Center, which Washington Post reporter Dana Priest focused on for a Pultizer Prize-winning series of articles about veteran medical care.
Priest told CBS Chief Washington Correspondent Bob Schieffer she spoke with doctors who worked with Hasan during his fellowship there.
"I don't think they believe that he was crazy," Priest said. "I think they believed he was very odd and that he didn't pose a threat. If they thought he was mentally ill, again, these are doctors. They would have given him up."
CBSNews.com Special Report: Tragedy at Fort Hood
At the same time, Priest said, the doctors and other psychiatrists who worked with Hasan worked under a different mindset than soldiers who served in other countries.
"They aren't necessarily like the infantry troops that are going to have the threat at the forefront of their mind," Priest said. "He's intelligent, soft spoken. No indication of violence. No speaking about violence. Very polite."
When Schieffer pressed her about reports that Hasan would make peculiar statements or carry around business cards decorated with letters that could stand for "Soldier of Allah," Priest said the public doesn't yet know whether Hasan was confronted about his beliefs.
"How much discussion was there among his supervisors and him about his interpretation of Islam?" Priest asked. "I think that's where the Army, you'll find, is reticent. I mean, they don't know enough about it. They may not even know enough about it to have a general discussion."
Priest told Schieffer she thought that the Army feared it would be politically incorrect to have such a discussion with Hasan.
"They're timid about that," she said. "The Army is very concerned about diversity in its forces. They need Muslim leaders. Right now they are trying desperately to increase their ranks of people who speak Arabic and who can help them in the Middle East."
CBS News National Security Analyst Juan Zarate joined the discussion when Schieffer shifted the conversation to President Obama's decision in the coming weeks about his Afghanistan strategy.
Zarate called the process Mr. Obama chose to follow in making his decision "indecisive and a bit weak." He noted the recent reports that the U.S. ambassador in Afghanistan discouraged the president from sending more troops to the country and an administration statistic that the United States pays $1 million per year to fund a single soldier in the country.
"There's a lot going on within the system, within the process to throw doubts into throwing more troops at the issue without a clear resolution of the strategy," said Zarate. "All of this, though, signals unfortunately, I think, a little bit too much indecision."
Zarate said the president will likely give a speech to Americans after the Thanksgiving holiday "to explain the number of troops and frankly to describe the strategy that the administration is going to resolve in terms of Afghanistan."
CBSNews.com Special Report: Afghanistan
Priest said Mr. Obama's strategy depends on his goals for the war.
"Is the goal to defeat al Qaeda?" Priest asked. "If that's the goal, well, according to my sources, there are only about 100 al Qaeda left in Afghanistan."
"One hundred al Qaeda in Afghanistan?" Schieffer asked.
"They're over in Pakistan," Priest said. "Again, if your goal is to defeat al Qaeda, then Pakistan is where you need to go. They've been very reluctant to do that.
"If it's not that, if it's more regional stability or standing up a stable political process, that is probably going to take a lot more than 40,000 troops, and more time."