aisle_s:

I don't know what you mean with "substantial proof", but there is really only one explanation offered by the game, and that is that Griever was created by Ultimecia in the final battle. Consider what Scanning reveals about Griever:

"Griever
In Squall's mind, the strongest GF. Through Ultimecia's power, continues fighting without vanishing."

Further, Ultimecia's Witch Embodiment powers granted her the ability to reach into other's minds and pull things out (as she often displays when completely removing a character's stock of a certain type of Spell). In the case of Griever, she simply manifested the thoughts she pulled from Squall's mind regarding what he believed to be the most powerful being in existance. This would be a great strategical move on Ultimecia's part. This is made even more plausible when examining what the japanese version has Ultimecia say:

Ultimecia: Your feelings, I shall summon the most powerful of things
[from them]! The more strongly you feel, that will be what shall torment
you. Fufu."

The japanese quote there is 'substantial' enough, I would say.

As for whether or not Griever existed before this as some mythical GF, it is possible. The Griever Ultimecia created based on Squall's ideas may have in turn been based on a real GF, but there really is no way of knowing. The important thing is that the Griever WE meet, was created by Ultimecia.