http://www.coindesk.com/bullion-dealer-amagi-metals-stop-accepting-fiat-currency/
I think it's less of a statement about fiat currency and more of a statement about inflationary currency. The US Dollar has lost value over the years because the government thinks that inflation is the way to keep the economy running. They think that if the currency constantly loses value, people will be more prone to spend it instead of saving it. All that spending keeps the economy running.
I've always thought that without inflation that people will still need goods and services of all kinds, so would still need to spend their money (not hoard it), and the economy would all balance out. This is kinda what I like about most cryptocurrencies, they have a set amount of coins that will ever be produced. In theory, over time the price shouldn't change with respect to goods and services.