This is correct.
A balanced cable has no advantage unless it is connected to balanced circuitry at both ends.
The advantage of balanced circuitry is that the two signal wires carry signals that are 180 degrees out of phase with each other, and the ground/shield carries no signal.
Any noise that is induced into the signal wires is induced into them equally, with the same phase, which cancels and is nulled out when the signals reach the balanced circuitry at the receive end of the cable. The balanced circuit only sees and amplifies the out-of-phase signals, the DIFFERENTIAL signal, and is totally impervious to the noise, which is NOT a differential signal. The noise is what engineers refer to as a "common-mode" signal, which the balanced circuit essentially does not respond to.
Originally Posted by JD in NJ
I could be wrong about this, but I believe that 'balanced' cables are only less subject to interference if the equipment at each end is also balanced.
This is why balanced cables can be run from a microphone, which often only puts out a few microvolts of signal, 100 feet or more to a balanced preamp/mixer unit, and have essentially zero noise. This is common practice in large auditoriums and similar recording venues.
If you tried that with an unbalanced cable, the noise might be louder than the microphone; bad hum and noise in most cases. 99% of the the signal voltage is on one wire, and this is easily contaminated with noise from many sources. From an engineering standpoint, an unbalanced cable is inherently a terrible design.
Unbalanced cables should always be kept under five feet if possible, and not used at all if possible.
Professional audio equipment always uses balanced circuits for this reason, and also top-quality home audio gear.