@HopelessDemigod Yeah, so I think that really helps to highlight the issue here, that you don't have money in the bank, rather you have a bank agreeing to pay you money, and if the bank fails then you have an insurance policy agreeing to pay you money.
I don't think this is splitting hairs. I think it is actually very important for people to realize that a deposit in the bank is a relinquishment of ownership of that money. It's important for a few reasons, ranging from the lack of accessibility to money that is no longer theirs through the social obligation of diverting tax resources to pay those insurance obligations.