Here is a thought i just had. What if Birgette's memories go farther back than she has said. What first got me thinking about this is one short half-sentance. Birgette says something along the lines of 'I remember hearing about a female warder'. Now this seems like the type of thing that would be remembered, similar to the fact that Aes Sedai were once both men and women.

So if it is as recent as the AoL then odds are there would still be stories about it around in this age. So therefore it must be pretty old. What if Birgette's memories go back one full turning of the wheel. Now i know that what I am about to say argues against my previous theory (Birgitte and the horn) but it is another angle that I have seen. Obviously the heros have not always existed. This is implied by what Artur Hawkwing says in Falme, something like "you may join us" when he is talking to Hurin (where did this guy go anyways? He seems to have just vanished) which implies that there are occasionally new heros. Maybe, in every life, the hero ends up facing a choice, as Rand has had, to follow his destiny, or run from it. What if every turning of the wheel, a hero has at least one decent chance, to stay a hero, or be like a normal person. If so then this could be Birgette's chance. She now has a choice. She has her level-headedness, which was balanced by Gaidal's rashness. Without that, i believe that Birgitte will be faced with a choice, in which she will have to choose between being level headed, or rash, and Gaidal will have a similar choice. Birgitte is losing her memories, as I believe that all hero's do at somepoint, or they would have memories of many turinings of the wheel. Birgitte remembers herself, exept since her memories are gone, she does not remember being a hero.

Or possibly she remembers the bonded Aes Sedai. Either way, her memories are apparently very old. Another point, as Birgitte talks about her memory of a female warder, she smiles a secretive smile. This could be hiding that she remebers this happening before, but loses the memories quickly, so she cant remember exactly what it is that she was smiling at, and can't warn anyone about whats going to happen.
Of course for this theory to work, not only does Birgette not need a Gaidal figure, but Gaidal has no need of a Birgitte figgure.