It is the thought that counts -- even if the thought might be a little strange, like protecting a waterbender from the rain. She could direct it away from them, if she really needed to.

"You act like Aang wouldn't tag along with him for the search."

Which bothers her as well. She can more than take care of herself -- and they'd be more concerned about her being off with Zuko than if she was simply off by herself. It's not like anyone else seemed to even realize she had wandered off because she was upset.