SirNickity:
No, that's how it's done. A common mantra around here is "tie ALL grounds together" because everything needs to know what +5v is in relation to (for example.) Same goes for audio.
If I had a multimeter and I touched one probe the the RCA - and the other to the RCA +, it would be able to read the voltage even though the multimeter's ground is not connected to the circuit. I see no reason an amp should need to share ground over an audio input to determine the voltage difference. And TI does have a document showing various "ground loop break circuits" for both input and output. And of course the transformer worked.
So that may be how it's done, but I question why it's done that way. Perhaps it has something to do with reducing interference? Or maybe it's just a cost reduction measure, keeping things simple? I don't know. I do know professional audio equipment circumvents this issue and the interference issue by using a differential setup though.