if the stereo signal you routed to the 1 input gets routed back to the other channel...they dont jump through air
correct, the only thing the left input ring is connected is the normalizing/switch pin of the right input socket. The right input ring is not connected to anything
In balanced that sleeve goes thru the "impedance balancing" to ground <- that is the circuitry you mentioned, which cancels the noise
that would be a resistor between the ground and the ring on an output socket (my virus uses 470ohm resistors for this), but that's not the circuitry that cancels the noise. That circuitry would have to be connected to the inputs and it would have to subtract the ring input signal from the tip input signal usually using an opamp.
Stereo is a different thing completely
this is what I was pointing to. The left virus input is a stereo input rather than a balanced mono input