I like your first analogy. Your second analogy, on the other and, seems to me to justify the action. I think Macy's would thank you rather than call the police, but that's just my opinion.
maybe they would thank you. Imagine though the day after, they had noticed security camera footage of a masked intruder wandering the store, and then taking merchandise out the door. They can't identify the intruder. They call the police. There is an investigation. They spend $$$ on a new security system. People are fired. Then some time later you wander in with a smile on your face and tell them how you were the one who cracked their system. I can see a scenario where they are furious with you and call the police, telling them that you have just confessed to a crime. Then police then say, hey buddy you committed a crime, you confessed to it, and now you are trying to say you did it "for a good reason". Good luck with that.
Bad analogy in this case because the school had no idea that their FTP server was even attacked in the first place.
Better analogy to what happened:
Imagine you steal the $300 shoes with your new fangled trick and the mall security do not notice at all. You come back the next morning with the $300 shoes in-tow and then they call the police.