Balanced inputs are not defined by whether two channels of a stereo amplifier are bridged or not. The concept of balanced inputs is that the input is a differential receiver, where the signals on each wire are equal and opposite polarity. Thr differential receiver subtracts these two signals to reproduce the original signal. The benefit over single ended signalling is noise rejection. If the cable is exposed to a source of electrical noise, that noise will be induced with the same polarity and amplitude on both signal bearing conductors, and since the differential receiver subtracts the signal on both conductors, it cancels out the noise, which is common on both sides of the differential pair. This is how the term “common mode noise rejection” was coined.