Haha . . . I think the best solution to all these conundrums is just to realize and accept that:
a) It's time travel. It will NEVER make sense
b) Even if it did make sense, no one has any personal experience (except for the fact that we are all traveling into the future . . . even as you read this very message . . . we-oo-ee-oo)
c) Even if someone did have a true, provable personal experience, the universe of FFVIII clearly works differently than ours (when was the last time YOU saw a Sorceress?).

Just one more thing I'd like to add . . . if you recall, in the battle with True Ultimecia, she rambles on and on about reflecting on your childhood. Perhaps everyone in your party (or maybe just Squall; it doesn't matter to me) sees a moment that they have forgotten because of GF. Thus it is Ultimecia's doing that Squall sees what he does. And, at the risk of starting a cheap, random, meaningless theory, we can say that if it was indeed Squall that inspired Edea to start SeeD, it was Ultimecia that wanted him to. So, in a way, it was Ultimecia who is the true proginator of SeeD (although SHE couldn't have known about it without it existing before, just like Edea, and Squall, and . . . ahh, my head hurts).

Hope that made sense.