The expression “fiat money” designates the myth of money as individually created (think of God saying “fiat lux”) while it is rather socially created: even if privately controlled, or centralized, its creation always requires the participation—whether active or passive—of the whole society.
Fractional-reserve banking works not because commercial banks “pretend” still to have the money they already loaned. It works because the representation of that money by different bank accounts remains mistaken for the same deposit money, which hence replicates itself among its different representations by those different bank accounts (or notes, checks, etc), in what I call a representational monetary identity.
One of the most important concepts by Marx is that of Commodity Fetishism:
Whence, then, arises the enigmatical character of the product of labour, so soon as it assumes the form of commodities? Clearly from this form itself.