If a group of people had enough military might to declare themselves independent and not fall to subsequent invasion, then it doesn't matter what the rest of the world "thinks", they are independent.

They may be independent in some sense but it still matters a great deal. If other nations don't accept your sovereignty you can't really have trade or diplomatic relations. Just ask South Ossetia, Novorossia or Transdnistria. These days it's pretty pointless to be independent if you can't have foreign trade.

I'm pretty sure most sub-regions wouldn't trade their political dependence for North Korean-style independence (but I admit to not knowing the hearts and desires of most people ;) ).

Well, there's the Abkhazia option where you become a weird pseudo-state with no recognition. It's not great, even if you have a big friend like Russia who does recognize you.