M and I happened across this little bit of advice on TV the other day.
It seems that most major banking institutions include riders on their mortgages and credit cards allowing them to arbitrarily raid your checking and savings accounts if all your accounts are held with them and you are late on a payment. They don't need permission and they don't have to warn you it's going to happen. Many banks are using this technique specifically when accounts are already low on funds because that allows them to collect insufficient funds penalties as well.
Therefore, it is entirely in your interest to make certain that no one institution holds all your accounts at the same time. No one ever plans to miss payments on their debt, but bad things can happen to anyone. Besides, when it comes to banks, we really have to do our best not to let the sneaky bastards win.