The bank doesn't hold a copy of your house, it holds a description of your assets (including contracts like money). And it's absurd to say that if something is your property, then also its descriptions are your property.
That doesn't add up even assuming that pure ideas can be property at all.
That comes from copyright, though. Copyright is arguably something different than property rights, and is a very recent invention. That's why no one blamed scribes for copying books.
You could make a case for private communication extending from copyright, but that's not what the parent claimed.
That doesn't add up even assuming that pure ideas can be property at all.