That sounds like it could be a legal question and should be responded to by an attorney.
I am not an attorney and nothing that follow should be regarded as legal advise.
You will need to read all that fine print on the account documents the bank provided. You most like should read the fine print on their website. Print the page if you find they can not touch your other accounts. Of course, all such TOU documents have the "subject to change without notice' gigantic escape hole for them.
In many (most) cases the bank reserves the right to seize the assets in one account to pay a delinquency of another account within the same company. Banks do not share a reciprocity agreement AT THIS TIME.
It is highly likely, if your mortgage was from a big box bailed out bank, they no longer own the mortgage. In that situation, the investor, who owns the mortgage does not have the same access to your other assets. They will have to seize them through the courts. Read the fine print. Banks are sneaky critters and seem to feel they can do what they please with impunity. You make want to have a chat with an attorney.
You are correct in realizing the banks ability to make off with your other assets, the assets you use to buy fuel and bread, makes the situation WORSE for the consumer.
Give great thought when you consider all those bundles and benefits. These banks are not benevolent critters offering you all this convenient stuff. It a tether to your STUFF! Borrow from one. save and pay your bills from another.
Same with your insurance. Best to use an insurance company that does both home and auto, but don't let one company do both. Yes, I know, the presumed savings are tempting. If State Farm can not insure your home. don't give them your auto business.
You'll thank me when you find yourself in a real bind. Well actually, you will have options and the bind will never occur therefore thanks will be unnecessary. So, I'll say, "You're welcome," now.
Donna, don't let your home go into foreclosure as you slip silently into the darkness. That is the worst possible choice.
Call me if you need help.
Annette Lawrence, Broker/Associate
Remax Realtec Group, Palm Harbor, FL