"Could not find valid value for id" upon returning from PayPal Standard

This may be the same as CRM-11119. When paying for an event using PayPal Standard and click the link to return to the site, you get a CiviCRM-001 error - "Could not find valid value for id". The payment goes through and the event registration is completed; it's just that somehow Civi/Joomla isn't getting the event ID from the qfKey.

This happens both on a client's site with his PayPal and on the demo site with my PayPal account.