Imagine you're the Hughes corporation. NASA comes to you, says "We both know the Earth is flat, but we need you to spend billions of dollars figuring out how to keep a balloon in the same position for decades to offer internet to people. Now, the balloon will of course be inside the atmosphere exposed to wind, but it cannot move so it'll need some sort of thrusters to keep it in place. Also, we have to simulate the latency of all the internet as if it's served by a geostationary satellite, so make it extremely slow and annoying to use." Hughes complies:
https://en.m.wikipedia.org/wiki/Hughes_Network_Systems
They also somehow simulate the position of the balloon such that the parallax places it where a geostationary satellite would be instead of a balloon. See Satellites
What is more likely? This story, or geostationary satellites existing?