No it doesn't apply to them. This is a popular argument from libertarians but unfortunately it is a purely ideological argument that has no basis in reality.
The aforementioned currencies are backed by the value of their issuer's economies, those economies are real.
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.
"So when Japan said they would accept Bitcoin for payment of taxes ... ?"
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)
> Gold, on the other hand, is just valuable because it is expensive to produce and has a long history of being valuable. ...
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.
Gold is valuable by itself and there is only 80-90k tons of it ever (plus some amount in the oceans). Gold would be used everywhere in the electronics in pure form if it was priced and widespread as copper or iron.
You have to pay your taxes with USD, so there's always a base demand for USD. Bitcoin has no intrinsic demand. It can go to zero because nobody needs it.
The aforementioned currencies are backed by the value of their issuer's economies, those economies are real.