In most countries, bank account numbers are not sensitive information. That is an american oddity.
They're not really secret in America either. I mean, the account details are on every check for instance.
I always stick to cashier's check for this very reason (and for accounting purpose).
They may get into legal trouble. My mom had her checkbook stolen that was in her luggage and the person used the checking account to pay for an electricity bill. She reported it to the police, but they had more important things to spend time on. When you can use someones else's checking account number to pay for a utility at a fixed location, you probably aren't worried about legal trouble when you are doing it.
But, in order to fix it, they had to close my account. This alone was more than $40 in inconvenience for me, but there was literally nothing else that could be done. I had no idea how my account information got compromised (or, even if it was compromised), and I’m not sure what I would have done had my account information been leaked again via the same channel.
I work in the american bank industry. Just the status that 'bob jones has an account here' is considered personal information.
This might seem silly, but there are good reasons for it.