look friend, they had to make laws outlawing bank runs. You know what that means? They don't have all your money. And not only that, but the state is willing to use violence on you if you threaten their right to not have all your money. This sounds cut and dry.
Unless they're referring to scummy mega-banks that exist by fucking over the little guy with random fees, hard to close accounts, and other scummy practices like Wells Fargo, BofA, etc.