So in doing a little more research here, I don't believe it has anything to do with the IPhone nor the radio unit since:
1. A MACBook works fine in our 2012 showing the song info (shows that the radio/display is capable of showing the info if it is received from the BT module)
2. My IPhone works in a 2010 CX-9 and 2012 Honda (shows that the phone is OK).
I believe it is an issue with the Mazda Bluetooth module (made by Johnson Controls).
Our 2012 has a Bluetooth Unit Model TG1866 DHXA with a SW rev of 03.03.000. Out friend's 2010 CX-9 (the samecar) has a module (that works) Model TE6966 DHXA.
According to the dealer, our car should have a BT module TG1866 DHX (no A on the end).
The service supervisor at our dealer is going to try and order a TE6966 and try it out in our car. Unfortunately, Mazda controls these things pretty tightly, and doesn't like to provide them for warranty repairs to dealers without proof of a failure so he's going to try and get one directly from United Radio. If he can't order one, I'm going to take my car in and complain the the BT module keeps hanging up calls to try and get it replaced.
If all else fails, I may consider ordering a BT module myself from the Parts Dept.