we've probably all seen it:
Somebody wants to know the distance between two points, e.g. New York and Moscow, so he holds a ruler against a world map and then he multiplies the centimeters/inches he measured by the nominated scale of the map. And we all know that he won't get the actual result in kilometers/miles unless it's a special kind of map projection – equidistant azimuthal centered to either New York or Moscow, two-point equidistant with at least one of the anchor points being New York or Moscow; or a cylindric projection with equally spaced parallels and he decides that he'd rather know the distance between JFK International and Concepción, Chile.

Some time ago, I read that "the 'Gott-Mugnolo azimuthal' has the lowest distance errors of any map".
Does that mean that if you use a Gott-Mugnolo azimuthal map to measure distances between two arbitrary points using a ruler, you'll still get wrong results, but on the average the result will deviate less from the actual distance than on other projections?
If the answer is "No": So what does it mean?
If the answer is "Yes": Is this really true for a world map or only for maps that cover smaller areas (e.g. a single continent)?
Kind regards,
Tobias