What you say likely holds true for Seanchan prophecies, like the Essanik Cycle, but the issue here is the Karaethon Cycle, a set of prophecies which predates both the Seanchan and Artur Hawkwing himself. It is also worth noting that there were corrupted 'Prophecies of the Dragon' on the Seanchan continent when Luthair arrived, which could mean that the Karaethon Cycle predates the Breaking. It could also mean that these are different Prophecies entirely, but because they are described as 'corrupted' rather than simply different, I am inclined to believe they were similar enough. If so, then this "pure" version of the Karaethon Cycle was discovered during the journey. And how likely is it that Artur Hawkwing, who hated Aes Sedai enough that he wouldn't allow one to save his life, sent a Foreteller on that ship?

Really, even if you do believe that the Karaethon Cycle was appended by other Foretellings without anybody bothering to note which texts were new and which were part of the original, that's already some terrible scholarship right there.