I have discovered- to my horror- there are still people who believe the Earth is flat. To compound my dismay, I see some justify their belief by saying government promotes the "globe Earth" theory, so it must be a lie.
Government conspiracies aren't imaginary; many are carried out openly, often in front of news cameras. If there's opportunity, an advantage, and low chance of being exposed and embarrassed before the lie has served its purpose, government will lie. The Gulf of Tonkin "incident" and the Tuskegee experiment should be evidence enough.
But, government also promotes-- or accepts and uses-- "2+2=4". A stopped clock is right twice a day- although this was more true before digital clocks.
Earth was known to be a globe long before NASA came along to "promote" the idea; millennia before any current government existed. This reality was discovered independently by various people throughout history, using experiments they were able to think up and do for themselves. Experiments you can do, if you care to.
If you don't want to measure angles to the stars or do other physical experiments, you can engage in thought experiments to the same end.
For example, look at "flat Earth" maps. The farther you move from their center, the North Pole, the worse they get. According to those maps, in Australia you would have to walk much farther to cover the same distance east or west than when walking north or south. I pointed this out and was told the maps aren't a true representation and distort the shape of the Earth, "just like maps of a globe Earth".
Yes, because the Earth isn't flat. Being nice, I suggested they make a flat Earth map without the distortion. It should be extremely easy. The problem in making a flat map of the world comes from trying to represent a spherical surface on a flat one; something will be distorted, usually near the poles. A flat Earth wouldn't have this problem and would fit easily on a flat map; a simple one-to-one transfer of points, without land or ocean distortions. Yet they can't do it.
You can approach their claim from multiple angles and keep getting the same result: a roughly spherical Earth.
When data from many different observations keep pointing to the same conclusion, you can be confident you've found truth.
Skepticism and an open mind are good, but falling for any hare-brained notion which sounds appealing isn't enlightenment. Even if it means you and the bad guys sometimes agree.