Sorry kijanki, I thought we were talking about discrete level or discrete within an IC circuit, and that the 3 op-amp instrumentation amplifier you showed was a different part of the discussion. The circuit shown is missing the output buffer that would be on a practical circuit and those two output resistors have to be matched as they dominate CMRR in the calculation. I now get completely where you are coming from :-)
If the noise current induced are not the same in both wires, then they are not common mode, they are differential mode, and a balanced connection only removes common mode noise.
As for the balanced connection - it is not balanced anymore when you
connect it to unbalanced input. Noise currents induced in both wires
will be different and noise will go thru.
In a typical connection of two components, you have multiple paths for current flow which is how CM noise generates a signal. With a catridge/phono stage, you have a single loop so induced common mode noise does not generate a signal. Where it gets dicey, is when you start adding new current paths like shields. Fix your DM noise, and now create CM noise. I think this is perhaps was jcarr was referring too?