We were clearly shown that her name was not crossed off in the lighthouse and we've been reminded that it was crossed off in the cave.
See, it's stuff like this that drives me straight up a wall. I hate inconsistencies that have no meaning, so it makes me want to say there must be some reason for this, so maybe I'm on board with the "Kate is a secret candidate" thing.
But, as far as we were "clearly" shown that her name wasn't crossed off in the lighthouse... well, yes, WE were, because we're rabid about stuff like that and scrutinize screencaps and stuff. But would a more casual viewer know that? I know I mentioned it to some people and they just gave me blank looks and said "How did you notice that?" (And I said "I didn't, ericd did." LOL.) So much as I hate to say it, it could be just a technical boo-boo about the lighthouse name. (Ugh, that tastes bad in my mouth just to say it...)