I'm sure having a nation-state is a major factor, but I bet it also has to do with the average wealth, geographic location, historical alliances. However, I'd put my money on skin color as the biggest factor.
If the UK is a country of countries then Greenland is most certainly an autonomous country. The Wikipedia article for Greenland has the word “country” mentioned 14 times, so I’m certainly not the only using the term this way.