I think the "right" way to display the distance would be from the closest points in the guessed and target territories. So United States and Canada, sharing a border, would be "0 km", while Canada and Mexico would be whatever the shortest path from border to border would be (like 2,000km?)
I have a feeling that's a bit more difficult than centers, though. But it wouldn't be a problem as far as outlying territories go; the image is of a contiguous landmass, not the entire country.