A decent question.
I think for me the answer would lie in the way religion was dealt with, as a child you believe what you are told but over the years incongruence's appear between what you are told and what you perceive, the fact that no two religions seemed to be able to agree is mirrored in FE with their maps and competing philosophies.
I think in the end it would be direct observation that would lead me to believe they were wrong, like JK... I am an amateur astronomer and watcher of the skies, two things stand out as being demonstrably wrong in the main FE world, sunsets; having watched countless times the sun sinking into the sea whilst being told (in the FE alternative reality) it doesn't, it fades away.
But also the subtle signs of roundness, earth shadow
http://www.atoptics.co.uk/fz973.htm ,eclipses , watching the night sky rotate, not only through a single night but through the seasons and the roundness of everything else we observe.