How has the problem of waiting for confirmations been eradicated?
Perhaps they are referring to the green address technique.  Some exchanges support this now:


http://en.bitcoin.it/wiki/Green_address


Or they might be referring to the ability to protect against a race attack by listening to many nodes so as to learn of any double spend race attack attempts.  That doesn't eliminate the risk entirely but helps to bring it to a level that the merchant can manage.  There has been progress towards doing this listening with varying results ( http://www.transactionradar.com and http://blockchain.info/double-spends ) but there is no service built yet for merchants that provides transaction monitoring and alerting when double spend attempts are detected:


https://bitcoin.stackexchange.com/a/2625/153