I don't think that's necessarily logical, the AI's in each person's BOTM game will be the same and follow the same AI scripts and logic. They may act differently - some of it might be due to differences in player-controled causes - such as meet date/location, religion, tech status, relationship, etc. But they are facing the same script, but REs don't work that way.
If everyone would be drawing from the exact same subset of available RE's, then your point would be logically correct - as all would be subject to the same possibilities though each game would still have different outcomes. However, if each game will have different REs in the pool, it is not so.
So, each player will be facing different random possibilities. This would be more akin to have random AI leaders that are determined separately for each player's game, something that doesn't happen in XOTM.
A player who draws the possibility of a Barbarian uprising is at a huge potential disadvantage to one who draws the possibility of a free Golden Age.
Drawing a chance to lose your pastures any turn is a massive disadvantage if someone else does not draw it, if you everyone had a 1% chance every turn it would be fair, but if one has 1% and the other 0, I don't think it is.
Lastly, you have the ability to alter AI behavior - through diplomacy, trade and war to name the most-obvious. But you can barely influence the REs and have no way of knowing what you're up against in any situation.