The aforementioned currencies are backed by the value of their issuer's economies, those economies are real.

If I can buy an item from Amazon or Overstock.com via Bitcoin or via Yen or via USD, explain how there is an actual difference.

Every American participating in that economy must pay taxes every year on their income. The taxes must be paid in US dollars, even if the economic activity uses a different currency or barter. Therefore Americans must come up with a quantity of USD proportional to the size of the American economy every year (or "go to prison"), and provided that the total amount of USD in existence is bounded (this part is the job of central banks) this places a floor on the value of USD. This story is necessarily simplified but I think essentially true.

There is an old saying that a language is a dialect with an army and a navy. Likewise, a fiat currency is a currency with a taxing authority.

Gold, on the other hand, is just valuable because it is expensive to produce and has a long history of being valuable. So that model can work.

I'm not able to find any reference to such a move, which I would think would be widely reported in English. So I suspect you may have your facts wrong. I read that Japan no longer collects sales tax on digital currency transactions, but that is not at all the same.

If, hypothetically, a major government accepted all tax payments and equivalents in XBT as well as their own currency, and credibly promised to keep doing so no matter what, they wouldn't so much be backing Bitcoin as "unbacking" their own currency. It would leave their citizens free to stop using fiat currency if they wanted, and if enough were eager to do that the value could go to zero. (In principle, that could be fine. In practice, contracts and other nominal rigidities would probably make the transition period... problematic)

If a major government decided to accept tax payments only in Bitcoin, they would be backing it in the sense intended.

(I'm not necessarily taking a bearish position on Bitcoin. Rather, I'm arguing that fiat currencies are not the right model for understanding its economics)

Bitcoins are expensive to produce and if it hangs around very long it will have a long history also. So in the long run bitcoin could be a viable alternative to gold.

Likewise, I own a $100 billion Zimbabwean dollar bill as a curiosity, but that market doesn't put an important floor on fiat currency prices!

Paper money or coins of little or no intrinsic value in themselves and not convertible into gold or silver, but made legal tender by fiat (order) of the government. [1]

Fiat money is an intrinsically worthless object, such as paper money, that is deemed to be money by law.

----

I will say that when Japan agreed to accept payment of taxes, with Bitcoin, they deemed it to be money.

Probably I could find examples in the U.S. government prosecutions of criminals who used Bitcoin, that had government lawyers advancing arguments that treated Bitcoin as money, but, I don't have them to hand.

I'm really interested in figuring out if this is true. What source is saying this? From what I can tell some taxes might apply to Bitcoin in Japan but in no way can you actually "pay" taxes in Bitcoin (you can obviously convert it to Yen first though).