If it's not linked to the true Twelve, the explanation is that Louisoix carved symbols into rocks and asked people to pray to them, and they did, and then he called on their prayers to power his summoning . Prayers + Aether = Manifestations. Isn't your question sort of like saying, "If Good King Moggle Mog XIIth is a myth, how do you explain that I just punched Good King Moggle Mog XIIth in the face?" We saw Good King Moggle Mog XIIth, but the Scions go on to question if he ever even really existed. How can we see the same event with the Twelve and just close the book?
We certainly have enough information to ask questions and point at possibilities, and even pick favorite theories to throw our weight behind, but to close the book on it as "It was The Twelve." ... If that ended up being correct, it would have been correct incidentally, imho.