No one said that. The conspiracy is orchestrated by space agencies.
Q: "Why do the all the world Governments say the Earth is round?"
A: It's a conspiracy
It's not a well kept secret that the round earth theory was out long before space agencies existed.
Our FAQ is out of date. Science had appeared to support the RET, then when the space agencies got into space, they discovered they were entirely wrong. That's partly why they faked everything-out of embarassment.
Q: "How did NASA create these images with the computer technology available at the time?"
A: Since NASA did not send rockets into space, they instead spent the money on developing advanced computers and imaging software instead
According to this site, NASA never got into space.
Also, had that happened the way you stated, they would have been shocked and euphoric about the earth's shape, and would have immediately sent glowing reports to 'enlighten' the world (especially since when we got into space, it was during the cold war space race: ie - THE PERFECT TIME TO ONE-UP THE SOVIET UNION). There would be no need for a conspiracy as the government would have given them funds anyway to develope a new, working space program based on your skewed physics.
The US/USSR couldn't agree on the simplest of things, and almost sparked WW3 several times....
So, in a nutshell, it's the common consensus on this site that the two superpowers had a secret alliance pact to keep this secret even when US/Soviet tensions were at their peak. Even though both sides were constantly trying to best the other. What better way to do that than find out the earth was flat and become the triumphant, enlightened society?