The song played on the show is called Don Quixote, maybe it's the same one they were thinking when they wrote spanish rain and just changed the title afterwards, or maybe spanish rain is another song. More than once coldplay have used kind of the same phrase in a song and later on on song title, like 'now my feet won't touch the ground' is a song name, but that phrase also appears on LiTii.. I've noticed the same happened in another songs, like they have a same idea going on in differents songs...
just a thought anyways.