The explanation doesn't even make sense. Even if the opposing magnetic pole were the other side of the "disk," magnets simply wouldn't act in the way they're trying to use to justify it. They wouldn't be horizontal, parallel to the ground (as we see on a spherical world). They would instead point vertically, perpendicular to the ground, no matter where on the disk you're standing; this is because the north side of your compass would oppose the northern side of the disk, while the southern side of the compass would be strongly attracted to it.
Notice how, on the spherical world, compasses act normally in most places, then strangely when you approach the apparent "pole" of the object. This is completely consistent with what we observe in the real world. You'll notice on the flat planet, though, that
the compass always faces the same way on any position from either side of the disk (only changing when you move completely outside of it). The disk idea makes no sense and was concocted by loonies with no idea how magnets actually function.