Your post pretty much proves why the UFC is correct in their policy: While it is true that Artsakh represented an "oppressed minority", it is also true that the Republic of Artsakh was "founded" by military conquest in contravention of international law. Legally, and as upheld by 4 UN resolutions, the territorial rights lie with Azerbaijan, which is why the international community had such a hard time condemning Aliyev even though his soldiers were committing a string of atrocities in their reconquest of Artsakh.
In other words, by allowing him to fly that flag, the UFC would have actively endorsed a contravention of international law. As an entertainment company and promoter of mixed martial arts sporting events, does opening such cans of worms make any economic, political or branding sense to you?