In the case of the former interpretation, I'd like to point you to two separate articles that take this assumption and run with it. The first is the famous "In Praise of the 6 Mile Hex" and the second is the more recent "The Properties of Hexes and Mapping," both of which I encourage you to read if you like this sort of thing. But I think I can make my point just by stealing one image from the first article. BEHOLD:
To some people, the utility of this image is immediately obvious. To others, it's confusing what purpose it would serve in play. The second article delves into this kind of math for a range of hex sizes, including 5, 6, 7, 13, 19, 20, etc. That's because the people using this interpretation are actually pulling out the yard stick and measuring the party's precise location within each hex, or they're measuring the exact route they move through each hex to keep a running total of the distance traveled, down to the mile (or half-mile, even). And if you play some of the oldest RPG hexcrawl content, it seems necessary. Take a look at these movement rate charts from OD&D and from the Greyhawk Gazetteer:
Some of you are going "well, duh." Others are like, "what the hell?"
Personally, I've always been inclined to do 3-mile sub-hexes and 24-mile super-hexes, so that you can have each super-hex measure 8 sub-hexes across. You can call a 3-mile hex a "league" and a 24-mile hex a "province" if you need to write rules that don't reference exact numbers, such as if you want to apply the same rules to a pointcrawl system or just a freeform map. You can also redefine them as 5 km and 40 km, respectively, and it works out pretty cleanly. The 40 km province will still divide into 8 "metric leagues" across!