BTC goes to payment processor which gives fiat to overstock.
So overstock actually accepts fiat.
The payment processor is
coinbase. On coinbase, a merchant has the option of keeping payments in their coinbase wallet, or enabling "instant exchanges", which exchanges it for fiat as soon as the customer pays. Does anyone know which option Overstock.com uses?
I think I may have found the answer, according to
this Wired article:
Before each payment is made, Coinbase sets an exchange rate, immediately converts the buyers bitcoin into dollars, and transfers the dollars to Overstock. The retailer never holds any bitcoin.