Why? I mean these are all automated hacks/breaches. I doubt a random password vs a regular one you use for several places would make a difference. Also, if this was a breach into the BA system, they would have access to the accounts no matter what password you choose.
If that is incorrect, please correct me. That is just how I understand this subject.
This is incorrect.
They could've stolen the passwords, and if they were not encrypted well (salted, hashed, one way encryption), can hack into all the accounts with the stolen passwords.
The breach may have been plugged up by now, but that doesn't mean that the stolen passwords won't work.
A new password will help if this is the case.