It is less of a dollar, because I can say you can exchange it for a dollar when you can not, in fact, exchange it for a dollar when you try to,because I never had enough(or any) dollars. In the real world when the bank runs out of dollars the government will give me dollars instead.
I think that is a fair critique, but that will be coming at some point, very likely. Either a law requiring 100% liquid reserves, or a law bringing them into the FDIC system.