No, UFC follows the rules of the relevant athletic commission and they only use referees (and judges, and timekeepers, etc.) licensed in that jurisdiction. UFC famously moved a fight from NV to CA because NV wouldn't license Jon Jones to fight after a drug test: https://www.espn.com/mma/story/_/id/25603991/ufc-232-moved-l...
I may be wrong, but I think it's the other way around. The commission sets the rules and hires the referees to enforce them. Dana White has be openly critical of certain referees and made it clear he'd fire them if he could. The UFC must follow the rules of the commission. I believe that's why some past fights could only occur in certain jurisdictions, and with modified rules. The unified rules of MMA are set by commission voters, not the UFC [1].
"Unified Rules" is followed by MMA organizations in the USA. It's a set of rules most state athletic commissions have agreed on over the years. It is a horrendous rule set and judging system for MMA.
"Unified rules of MMA" were developed at the state athletic commission level (NJ maybe?), but not everywhere implements them: https://www.mmafighting.com/2019/4/16/18358920/abc-survey-at....
The ending of one fight in TX had betting implications because of their odd rules. https://www.mmafighting.com/2022/6/21/23177038/texas-commiss...