It workded like a charm with the 2010 model but not with the 2011 Santa Fe, so this leads the dealer to come to the conclusion it must be an Apple or iPhone problem?
You can rule out ATT since ATT has notthing whatsoever to do with this.
Are your iPhone contacts synced with the Sante Fe via bluetooth when your iPhone is connected?
Either way, the voice recognition is being done by the Santa Fe system?
If so, not sure how this is an iPhone problem. Does this Hyundai system include the "made for iPhone" certification? If so, Hyundai certainly bears some responsibility if not all responsibility.