I skimmed over this PDF, and the first thing that jumped out at me, is that the closest path from one point to the other on a globe, is not necessarily east-to-west, or north-to-south, but a straight line. I'm sure anyone here knows this, but if you take a piece of string, put your thumb down on Point A, then pull the string taut to Point B, your string will track a route that, depending upon where Point A and Point B are, goes over the North Pole, passes Alaska, passes Iceland or Greenland, and so on. And as counter-intuitive as it seems, the closest point to Africa in the Lower 48 is not Florida, not Cape Hatteras, but... the coast of Maine.
And airliners stay within a few hundred miles of land if at all possible, even if it deviates a bit from a "great circle" path, to-wit, again, flying in an arc over Greenland and Iceland. I've done it twenty times myself (ten trips to Europe, round-trip). When you look down over Greenland, all you see is whiteness, no way whatsoever to tell distance.
Granted, flat-earth models centered on the North Pole would return similar findings.