Absolutely it is: it is based on the trust we all have that the government will do whatever it takes to guarantee the value of a dollar. Me being able to commerce with you in dollars and not, say, in old zimbabwean dollars rests on the shared assumptions that the US State can and will be there.
We're playing with words now but the power of the dollar does not arise from your faith in it, it arises from the nations around the world that view it as a stable medium of trade. This stability is based on the employment and perception of ability to employ hedgemonic hard and soft power. The US isn't going anywhere because it has the guns, bullets, bombs, allies, trade, and diplomacy to stay in the top spot. Your faith is a product of that system, not a cause of it. Your faith won't build aircraft carriers.
We're not talking about the same thing. You're talking about why the dollar will be stable (and I totally agree with you there). I'm talking about why you and I can do business in dollars, and that was the origin of the discussion: bitcoins are made for people who can't trust each other. With fiat currency we still don't trust each other, but we both trust a common third-party, and have good reason to trust it, at least on the "it will be there" side.
