Balanced wires also reject noise that isn't coming from a ground loop. The two conductors are twisted closely together, so any interference radiated into the cable is picked up equally by both. Noise is the same on both wires, so the equipment can't hear it. Noises from nearby video or computer cables are picked up on each conductor. But remember, a balanced audio input cares only about the voltage difference between the two wires.
Interference is radiated equally into each wire.
The balanced input can't even see that the noise is there. The four wires form a tighter, more consistent pack than two wires can and can resist even more noise. You can't tell a wire by its connector. Balanced wiring is sometimes called XLR wiring because it often uses that kind of three-pin connector. But it's dangerous to assume that an XLR plug or jack is balanced.