If by "moving rendition of Aerith's Theme" you mean "My Hands from her album Echoes", I have to say I LOOOOOOOOOOOVE that song. I'm a Leona Lewis fan, though, so maybe I am biased.
If you are not talking about My Hands, link me to what you are talking about because I can't find Leona Lewis + Aerith's Theme anywhere on youtube or google.
I'm in the "it doesn't quite fit" boat, too, but I think the Japanese pop ballads don't fit either. I mean, other than Eyes on Me, none of the Japanese songs had anything to do with anything going on either; they were just all "oooooo love and stufffffff~"
My Hands is still a ballin' song though, I lurv her.