hmmm... not sure to what you are referring... seems like you get it.
Signal Symmetry refers to a condition where the signal on two conductors is equal but opposite in polarity. If it were a simple sine wave then the positive line would reach it's maximum at time t, and at that same time t the negative line would reach it's minimum.
When you take the difference you would twice the maximum excursion of either one of the lines - so if the sine wave was swinging from -1V to +1V on the "+" side, and +1V to -1V on the "-" side then the output of the difference stage would be 2V, which is 6dB greater than 1V.
At the same time, the noise that is induced into the system - or cable - will be equal, and of the same polarity on both sides of the line, so when we take the difference we'll end up with no noise voltage. That, of course, assumes a perfect system, which doesn't exist, but there will be a significant rejection of noise induced into the system when we do this. HOWEVER, and this is important, a differential stage works best when it is balanced.
Signal balance actually refers to impedance balance. The impedance from each source pin to ground must be very nearly equal. The impedance from each input pin to ground must be very nearly equal. And the impedance of each path must be very nearly equal, since the combination of a source impedance, line impedance, and input impedance is a series circuit.
Some input stages are remarkably tolerant of an impedance mis-match, think transformers. Others introduce an impedance mis-match - thing the single op-amp topology. Many really bright folks have spent considerably brain power figuring out tricks to make the inverting and non-inverting inputs of an op-amp 'look' the same to a signal. Some of those tricks work, some don't.
A single-ended source can drive a differential input - it won't have signal symmetry, and it may or may not be balanced, or rather the degree of balance may be compromised. At which point the ability of the input stage to tolerate imbalance becomes the key.
Last dead horse to beat - shielding vs twisted pairs... shielding can prevent RF energy from reaching the signal conductors. It can do nothing to prevent magnetic energy from reaching the pairs and inducing noise currents. If the shield is grounded at both ends then current can flow, and if the shield is improperly terminated at the input it can introduce noise.
This was the reason folks started connecting the shield at only one end (telescoping shields). However, a shield - or any conductor - that is grounded at only one end is an antenna. You have to pick your poison some times.
Twisting the signal pair helps to reject magnetic fields. If the twist rate is uniform then each conductor is exposed to the same magnetic field, which provides some additional rejection. And then of course there is the balanced, differential input stage to finish the job.
So isn't that basically what you said - only i used more words<G>???