The demand for USD comes from the legal structures that exist in the United States for things like debts, torts, taxes, etc. Basically, if you take out a loan to buy a house, you have a legal obligation to repay it regardless of how it is denominated by your bank; but if you fail to meet that obligation, you will need to deal with a bankruptcy court, which will only deal in USD. So if you take out a 40BTC mortgage and fail to pay, the judge will first convert the value of the house into USD and work out a way to repay (all or part) of the debt in USD. By forcing you to convert what assets you have to USD, the court is creating demand for USD.
Of course, banks know this (it is the core of their business) and will therefore denominate loans in USD to avoid the risk of an unfavorable conversion during such a proceeding. Such an unfavorable conversion is exactly what the creditors in the MtGox bankruptcy are facing, because the proceeding involved converting their BTC accounts into JPY according to the exchange rate in 2014. Due to the change in BTC prices recently, that means that under the law the creditors will be fully repaid using what BTC assets MtGox still has, despite the fact that the creditors would receive a far greater payout if they received the amount of BTC that had been in their accounts at the time of the hack.
Beyond debts, there are also torts. Suppose I crash my car into your house and you sue me for the damage I caused. The courts will order me to pay in USD; so again, the courts are creating USD demand by creating an obligation to pay with USD.
So the demand for USD is only indirectly due to demand for goods and services; after all, there must be some reason why merchants are pricing their wares in USD. The direct driver of demand is the law itself, hence "fiat" currency.