In order for twisted pair with a balanced receiver to cancel noise both lines have to have the same (nearly exact if not exact) impedance characteristics, if they do not then the noise induced on each line will have different levels, frequency response, phase shift, etc and will not cancel out with the balanced receiver. You do not have to have an inverting signal on the inverting leg, it will work without. The reason it is called balanced is referring to the balanced impedance, balanced differential means balanced impedance with differential audio signals on each leg.
Here's a helpful doc....
https://drive.google.com/file/d/0Byu...ew?usp=sharing
Fig 2.4 is what I ended up doing in my car.