Even if it was talking about airplanes, it doesn’t mention “surface”. So it would still hold, given that airplane parts aren’t infinitely thin.

Though if you fly economy it seems like they're bent on approaching it as a limit.

As long as they don’t actually reach the limit, the proof still holds.

Topologically, an airplane is identical to a universe of curvature=+1. Since the size of the grid versus the airplane/universe is not given, I will assume there are infinitely many grid points.