Balanced means that the + and - amplitudes of the signal are referenced equally to ground.
Not a requirement when using transformers which are not center tapped, as was the case for many decades. In the old days, you'd use a single amplifier output, to drive one side of a transformer, and the resulting output had no reference to ground, only to each other.
It is only in modern times that we can use multiple op amp stages as the sender and receiver. And still, the receiver does not rely on any ground reference.
Best,
E