This doesn't follow. By this reasoning, noone should pursue FRNs because they have no inherent value. People buy gold for a number of reasons. As erowe correctly pointed out earlier, gold, when used as a medium of exchange, is fiat. What makes gold money different from paper is that gold can't be printed. Thus it serves as a store of value, which FRNs don't.
If gold is fiat, then all money is fiat. Why then even bother criticizing the true fiat currencies, if we're just going to change the definition of all money to fall under that umbrella definition? Perhaps you should look up what fiat really means.
Of course any "accepted medium of exchange" is going to draw additional value from being one of the rare commodities that enough of society thinks is worthy of being a medium. That doesn't make it fiat, it is a feature of how money happens naturally. You have something with the desirable characteristics to be a convenient means of exchange, one that solves the inherent problems of bartering (and as we know, gold has many characteristics that make it an ideal source of money, such as scarcity, durability, portability when compared to other commodities, etc.).
And finally, I must ask, are there any more noteworthy countries that even use a gold standard anymore? Even if there are, the vast majority aren't buying gold just to sell to them... Yet gold is still considered valuable without being a currency. No matter if you think it should be valuable or not, it undoubtedly holds value on its own.
It's pretty simple how it holds value on it's own: Uses as commodity + costs of production + scarcity + long history of accepted value and desirable characteristics = market value (without even getting into supply/demand curves, though scarcity has an effect on those). Who gives a crap about "intrinsic", when the market has spoken. It's valuable, and not just because people say so. People see value in it without it being sanctioned anymore. That's anti-fiat.
All of those reasons (and that's just scratching the surface) makes calling gold fiat a pretty baseless claim. People who support bitcoin would be wise to shy away from trashing gold, because all it's doing is working to de-legitimatize any alternative currency.