Overstock.com uses Coinbase and Coinbase handles the entire checkout process. It's really no different than checkout with PayPal. Except that it's never in bitcoin at all. Overstock never shows a bitcoin amount due, it's handled entirely at Coinbase's end. And no bitcoins are ever given to Overstock.com, they just get USD from Coinbase directly and the customer is charged the amount in bitcoins that convert to the amount of USD that their order is.
It's a win win for Overstock.com, really, since they don't need to worry about the volatility and instability of bitcoin and only deal in USD but get to look forward-thinking by accepting bitcoin. Yes, they are accepting more risk because Coinbase.com could disappear overnight (FAR more likely than PayPal or Visa disappearing overnight), but they get some advantage for their risk.
It's a win win for Overstock.com, really, since they don't need to worry about the volatility and instability of bitcoin and only deal in USD but get to look forward-thinking by accepting bitcoin. Yes, they are accepting more risk because Coinbase.com could disappear overnight (FAR more likely than PayPal or Visa disappearing overnight), but they get some advantage for their risk.