Well, if everything so far hadn't been enough hints, the bit about the hate reminding her what is means to be a true hero was confirmation enough. At least, this revelation calmed her down enough that she didn't pay attention to the poor person in charge of the chest mini-game.

"... So you are a friend of Link, are you not?" She asked as she still looked at the hat before looking back at Zelda. Even if they probably weren't thinking about the same Link.