but I would highly doubt that it would be something so lenient as to let people go running their mouths about everything that went on while they worked there

All of the information that the White House wanted redacted is already in the public sphere. If anyone was "running their mouths," it was administration officials. Please read this (note the citations for all of the redacted information, on the left of the page):

Indeed, the deleted portions of the original draft reveal no classified material. These passages go into aspects of American-Iranian relations during the Bush administration's first term that have been publicly discussed by Secretary of State Condoleezza Rice; former Secretary of State Colin Powell; former Deputy Secretary of State Richard Armitage; a former State Department policy planning director, Richard Haass; and a former special envoy to Afghanistan, James Dobbins. (emphasis mine)

These aspects have been extensively reported in the news media, and one of us, Mr. Leverett, has written about them in The Times and other publications with the explicit permission of the review board. We provided the following citations to the board to demonstrate that all of the material the White House objected to is already in the public domain. Unfortunately, to make sense of much of our Op-Ed article, readers will have to read the citations for themselves. (See links at left.)

In other words, the Times showed the White House that all of the information in the article was in the public domain already, yet the White House still wouldn't allow it to be published in its complete form--even after the CIA had already cleared the article. Why do you think this might be?

Also, please note, the government is not a corporation, so your analogies to corporate NDAs and corporate espionage are not relevant.