Um, no. The US dollar is backed by US law guaranteeing that it must be accepted as payment for all debts and by US law requiring taxes to be paid in USD. All of which, as the parent post points out, is dwarfed by the backing provided by all the merchants, banks, and consumers in the world who are using USD today. The corner grocery store in Pottsville, PA backs the USD by accepting it as payment for frozen pizza and toothpaste. The drug dealer in Venezuela backs the USD by accepting payment in $100 USD bills. These are the most important backing for the USD (the "Nash equilibrium" that the parent post mentioned.
And that kind of backing is what the community is TRYING to build for BTC.
> The US dollar is backed by US law guaranteeing that it must be accepted as payment for all debts
I believe this doesn't stop people from creating special obligations through contracts that are denominated in other currencies. It more means that if I run over your mailbox and a judge orders me to compensate you, I can use dollars.
Precisely. It means that if you sue me for ANY reason (including failure to live up to my end of a contract) the state will allow me to pay in dollars.
> The US dollar is backed by US law guaranteeing that it must be accepted as payment for all debts
If you're referring to the 'legal tender for all debts public and private' clause on the notes themselves, that means that it can be used for such purposes, not that it must be accepted. If we agree that I'll do your deck and you'll give me your car, you can't just say 'I want to keep my car, here's some cash instead'.
> it can be used for such purposes, not that it must be accepted
Before the contract is agreed to, the parties can make any arrangement they want, including agreeing to pay in bitcoins. But if one party fails to deliver and they wind up in court, then the court (as kragen pointed out) will almost never require them to deliver the item, the court will instead require that the victim be compensated and will allow dollars to be used to compensate them.
Now, if bitcoins were worth $250 each at the time the deck got painted and are only worth $160 each by the time the court case completes, there is a fairly good chance that the court will demand the $250 price be used to determine what the compensation should be.
Generally speaking, if I say that and you take me to court to get my car, the court will award you damages, which I can pay with some cash. The alternative, where the court orders me to give you my car, is called "specific performance" and is very rare.
And that kind of backing is what the community is TRYING to build for BTC.