The Scourge literally summoned Archimonde and helped them at the Battle of Mount Hyjal.
People have been aware that the Scourge and Legion are in league with each other.
Nevermind that Kil'jaeden ordered Illidan (again) to destroy the Frozen Throne, so Kael'thas should at this point have put 1 and 1 together and realized that the Legion may be behind the Scourge.
And that also doesn't even account that Lore books all over Azeroth said the same thing, so it's not like that this was somehow secretive knowledge by the time of TBC.
https://wowpedia.fandom.com/wiki/The..._the_Lich_King
Kael'thas recognized Night elves in TFT and greeted them in Darnassian, i think High elves were aware of their (former) home.
And the Sunwell had been enchanted in a way to avoid detection from Demons, as to not attract them (again), the Runestones in Quel'thalas exist for this reason.
You do realize that Illidan and Kael'thas were allies for some time?
And Kil'jaeden didn't tell any lies (at least on screen) to Illidan in regards to the Frozen Throne, he literally calls the Lich King "My creation".
C'mon, Kil'jaeden being the Leader of the Burning Legion wasn't secretive knowledge, as if KJ could just pull a "Uhm, someone else did this!", when Azeroth just recently been subject to a massive demonic invasion.
That may have been the state at launch of TBC, but even the Scryers, the only friendly blood elves on Outland had abandoned Kael'thas before we even got to Hellfire Peninsula.
As said, the entire situation is murky at best.