No, it's not necessarily true for a currency backed by a state, since the state can force you to pay taxes in that currency, thus creating demand for the currency and underpinning its value.

Tell that to Zimbabwe, who still doesn't have a national currency because of exactly this:

http://en.wikipedia.org/wiki/Hyperinflation_in_Zimbabwe

Its also true for every currency that is a physically scarce and useful resource, though being such a resource (or, alternatively, being designated legal tender and demanded for tax and other payments by a large and significant government) substantially reduces the probability that belief that the currency is worthless will become widespread.