imhififan, Yes, the circuit of the BAT makes balanced sense, assuming the description is accurate. If you want to get crazy, ideally you want the conductors of both phases of the signal to be "the same" kind of wire. For an SE IC, the ground side conductor is often the shield itself. So the positive and negative phases of the signal are riding on different types of conductor, if such a cable is used for a balanced connection. Can you hear that? I dunno.
But some good SE cables do use an audio ground connection via the same wire used for the hot side. In that case, the shield will not be connected to the audio ground wire, and using such a cable for balanced is "better".
Atmasphere can feel free to correct me if I am in error here.