Ah, that makes a lot of sense.The ground connection, in fully balanced case, is routed via the cabinets so does not enter the audio path.
Only the balanced signal is used for the signal itself and being balanced is immune because hum will be mostly common mode which cancels.
With this circuit the ground circuit is connected to the ground of the RCA so any ground currents go into the audio path.
So then, what is the purpose of grounding pin 1/shield of the XLR input? Since the op-amp input is differential, the ground reference voltage doesn't matter for our purposes.
Suppose Pin 1/the shield is not grounded to the ground of this circuit (but remains connect to the source ground)? I would expect this solves all the hum problems, but does it induce a safety issue -- we don't care about grounding on the op-amp circuit side since it only deals with 12V? I don't think any RF issues would be induced because we are grounded on the source side.