They aren't "hiding a Flat Earth". They are perpetuating the idea that Space Travel is possible, which they had to do to win the Cold War. They are simply mistaken on the earth's shape.
It goes a bit beyond that though, "they" are somehow faking things like GPS and Satellite TV and the ISS.
The airline industry are using great circles as part of their flight path planning.
"They" are pretending a lot more than just that space travel is possible.
And wouldn't it have been easier of the US to call Russia out on Gagarin and Sputnik if they were faking it too? And why are all the other space agencies now faking it?
It's just all too ridiculous to be plausible. Do you think the conversation went:
Sky TV: "Hi, is that the European space agency?"
ESA: "Yep, how can I help?"
Sky: "I hear you can put things into space?"
ESA: "Certainly can. Piece of cake, mate".
Sky: "Cool! 'Cos we've got this idea to have a satellite in orbit to beam TV into people's homes. You can do that, right?"
ESA: "Er..."
Sky: "We'll pay you!"
ESA: "Er...sure, we can do that."
And then what, a panicked conversation took place in the ESA about how they're going to fake it so millions of people can think they're getting TV signals from a satellite. As I've said before, the dishes in Sri Lanka when I went there with work were pointing up noticeably more than they do here which tallies with a geostationary satellite above the equator. What are they pointing at?!