Using a system for the purpose it was designed isn't misuse. Using that system with a bot when bots are prevented in the terms of service is a violation of that contract. Let's assume they've put that in (if they haven't, they have no case. Assuming they have, they can execute the penalties in that terms document for bot usage, such as closing accounts, charging fees, whatever they think is best and can get customers to agree to. However, it's not computer hacking. It's a violation of what they want.
"I know this is a leap so far I've practically already broken my legs and popped my knees, but it feels very much like 'if it wasn't locked they can't complain someone let themselves in'"
You are entirely correct. You've leaped so far that you're in orbit. If it wasn't locked, but they don't have permission to enter, then the law says they're not allowed to enter. This is a lot more like "it wasn't locked, and there is a big sign saying that people are allowed to come in, and people do come in and we like that, but someone came through with a bicycle and we don't like those". If it's your property, you can tell people not to come in with bicycles even though they're allowed to walk in. You can make them leave if they do so anyway. It is your rule, not the law, that says this.