Who else but the Nerevarine could have had the importance to satisfactorily been the one to kill Almalexia? Besides, it's simply better from the narrative standpoint to have her killed by the reincarnation of her husband who she may or may not have helped murder.
Knights of the Nine, on the other hand, would probably be just fine with someone other than the Champion of Cyrodiil doing the questline. Same goes for Bloodmoon not needing the Nerevarine, I think.
Nobody could have done it, but that doesn't mean the Dunmer people know that.
Considering Tribunal's MQ was was part of the 7th vision of the 7 visions I would assume it was The Neravarine who did it considering it was his/her destiny.
To quote the prophecy part of the prophecy
" Seventh Trial: His mercy frees the cursed false gods,Binds the broken, redeems the mad.
One Destiny: He speaks the law for Veloth's people. He speaks for their land, and names them great. "
Frees the cursed false gods, now that definitely happened. It doesn't say anything about killing Almalexia. Now again, the Nerevarine did that. It's the only reason Almalexia will even talk to you, so the Tribunal MQ couldn't have been done by anybody else. However the last sentence is equally important.
He speaks the law for Veloth's people. He speaks for their land, and names them great.The Nerevarine never spoke the law for Veloth's people, the Nerevarine never made the Dunmer great... So obviously despite what Azura might claim,the entire prophecy has not yet been fulfilled.