There are also quite a lot of references about records being burned/ wiped clean by Daedra/ competing nobles/alliances. Not every pretender to the throne is going to be recorded. Even Varen Aquilarios' records are probably being burned by some Daedroth. There are even quests where books and records/ land titles and ownership get burned and there are comments how that might cause problems in the future when the progeny of the current nobles lay claim to lands without any proof. In fact there is even someone who mentions that Varen's records are being purged as we speak.
It is a dark time of war and especially in the Imperial City everything is being destroyed or pulled into Coldharbour.
It is also to be noted that the alliances don't originally all know about the Planemeld, otherwise they wouldn't be fighting each other. It is part of Molag Bal's plot to distract the alliances whilst he goes on absorbing Nirn. It took a lot of secret meetings and convincing to get the 3 leaders to do something and eventually it was the Mages and Fighters Guild who banded to do something. All in secrecy and I am pretty sure any confidential documents are not gonna be public knowledge 1000 afterwards.
Yes, one should be weary of possible inaccuracies or silly things happening but as people mentioned above, it simply might get mentioned in the next game with a "convincing" explanation. Like the Dragon Cult being introduced in Skyrim.