Finally I got this fixed!
After I posted this message, I upgraded to iphone 5 which unfortunately had the same problem. I also tried unsuccesfully various flash drives (with mp3 files on them), and an old (but working) iPod Nano. After a few visits to the dealer (for routine maintenance), one of the service managers found a new firmware fix PI0693c which was just announced in the December 2012 TechLink: http://sandyblogs.com/techlink/wp-content/uploads/2012/12/December-Techlink-2012 -F.pdf.
In any case this firmware update affects the 2012-2013 Terrain, Equinox, Volt, Verano, Regal, Malibu, LaCrosse for various issues related to the radio/bluetooth connectivity. After about 20 minutes of reprogramming and testing out 2 of the service guys' ipod/iphones, it's been working.