First thing I should point out to you all is that the woman telling Kairi this story isn't really her grandmother. For those of you who haven't completely paid attention to the story line, Kairi randomly showed up on the Destiny Islands with no memory of her past and no family. From what I remember correctly, she was taken in by the mayor and his wife. The woman telling the story could just be the woman who raised her. As for connections to the secret FM+ ending, it's quite possible. Nomura is known for not putting something into a gamehat unless it has a direct connection with the story line. So chances are high that the story that Kairi and Sora are told and the secrect FM+ ending are connected in some fashion.
However, that doesn't throw out the idea that Kairi could be related to one of the three knights. It just throws out the idea that the older woman was related to them, but not entirely.