I'd argue that all currencies are by some definition "fiat," in that
no currency has ever had nor ever will have an objective value. A dollar -- or a bitcoin or a gold nugget -- is worth what we believe it is, and in every case that belief requires some level of trust, usually in one or more institutions. Believing in the Federal Reserve or the US Government isn't intrinsically more (or less) silly than believing in private banks issuing certificates that they assure us are redeemable for fixed amounts of gold, or for that matter believing that the gold itself is valuable. (There's no reason gold is a better backing for currency than silver, shells, or salt -- all of which have been used as legal tender.) Bitcoin's novelty is in attempting to take institutions out of the equation, but it ultimately hasn't taken away the requirement of trust -- and its wild volatility at least raises questions about whether institutions trying to actively manage the value of currency are actually such horrible things.
TL;DR: the phrase "fiat currency" annoys me. :)