We're missing the big picture here: that even if Tom was right (and that is a huge round earth-sized "if") he is arguing that NASA is part of a conspiracy on the scale of which has never been pulled off in human history.
Watergate involved a handful of some of the most brilliant minds in the world, but they couldn't keep something as simple as breaking into a hotel a secret for more than a few years, just to put things in perspective.
Tom, this is the government we're talking about. They SUCK at this kind of stuff.
Most people can agree that the military doesn't have a problem with keeping military secrets, secret.
Please recall that NASA was originally part of the military, being directly funded by the DOD and existing as a branch of the Airforce.
After it broke off into its own entity, to pretend to be a "Peaceful Civilian Space Program" with its motto of "For all Mankind," NASA remained operating in a compartmentalized manner just like the military. They use the same protocols for classification as the military, for example. They classify documents either Confidential, Secret, or Top Secret, just as the miliatary does. Astronauts are all military men with Top Secret clearances.
Civilian Space Program, indeed.
Keeping a secret at NASA isn't too hard when everyone is in the dark about what they're being told to build or write, what it will be used for, and the bigger picture. Military always keeps the snake's head centralized at the top of the organization.
And even then the structure of the snake's head is often decentralized, as just because you're a manager and have Top Secret, it doesn't mean you have access to everything, or even very much. The Military generally keeps everything on a need-to-know basis.