There is a misconception with the stretch of the conspiracy, mostly due to a disagreement within the FEer community. Granted, I find it most logical that NASA does not control the government of any country (they are only given money by the government), and has minimal control over things not concerned with their immediate responsibilities. Obviously, there are exceptions, but most things (education, airlines, et cetera) autonomously run under the assumption that the Earth is round, without NASA having to pop their head in all the time and go, "DON'T FORGET THAT THE EARTH IS ROUND!!" Logically, the conspiracy should only encompass what is necessary. It has its roots in some science, and a few minor things, but mostly the conspiracy doesn't extend beyond what it needs to. And the congress isn't a place that it needs to.
And sure, the extra budget would be nice, but what a scandal it would be if NASA was found to be manipulating/bribing/coercing politicans into giving them the extra budget. I just don't see why they would take the risk.
~D-Draw