I've always thought the title Amyrlin Seat was telling evidence against the 3rd Age Aes Sedai being related to the 2nd Age Aes Sedai. In the 2nd Age the leader of the Aes Sedai was called the First Among Servants (or whatever the old tongue translation would be) and sat in the High Seat wearing the Ring of Tamyrlin. In the 3rd Age their leader is simply the Amylrin Seat. Now, I gotta assume that someone who was taught the traditions, beliefs and abilities of the original Aes Sedai would at least know what the proper title of that order's leader was. More likely someone heard a garbled tale of the AOL Aes Sedai from her grandmother, who heard it in turn from her own grandmother and put together the phrase "Amyrlin Seat". This person would have been one of the founders of the White Tower, and if they got the leader's title wrong, how much else must we assume they got wrong?

I'd certainly be interested in getting Rand Sedai's opinion on this matter in the final book.