The new invite reg was effective Oct 1, 2012. You can still do refundable tickets for a visa. It's not a sponsor (like a business visa) , but a personal invitation letter, so I got my tourist visa w/out tickets. I'd be questioning the language on the website as in "transiting THROUGH". But, if it's a "destination", they may not allow you to even board in the US due to nonrev ticket. (no guarantee you'll be able to exit in a timely manner)
I hope you can figure it out.