have a legitimate case for a state
Let's see: They are mostly Christian in a majority Muslim country.
Mostly because the Armenians practiced ethnic cleansing after they took over the region...
Again you demonstrate your ignorance of the Caucasus. Karabakh has a huge Armenian majority and this has been the situation for a long time.
The Armenians did occupy a rather large area inhabited by Azerbaijani and its population was largely expelled, but this was after a war started by Azerbaijan to conquer Karabakh and after most of the Armenian population outside of Karabakh was expelled.
All in all, there isn't a case in the Caucasus where the right is so clearly on one side and of course Nagorno Karabakh should be internationally recognized.
An interesting trivia: The Soviet commission on nationalities decided unanimously in 1921 that Karabakh should be part of Armenia, but Stalin, the head of the commission, overruled them and gave the region to Azerbaijan. Rather funny when one considers who is most opposed to any recognition...