Discussing about the probability of wacky conspiracies is absolutely the wrong way to disprove this. The correct method is a telescope, a quite wide sign with a distance scale drawn on it in very visible colours, and the closest 200m+ body of water you can find.
As long as you are close enough to the ground, the curvature of the earth is very visible, even over surprisingly small distances. I have done this as a child.
Actually, assuming many-worlds and Higgs-Boson-ends-the-world, the world could have ended every time a sufficiently powerful cosmic ray hit the ground in a way that Higgs boson formed. We just live in the branch where that never happened.
(sorry for late reply)