The ADC has a typical CMRR of -120dB due to laser-trimmed resistors and balanced impedance with low input currents giving a ratio on the order of 6 decades of rejection. This gets degraded by the mismatch of the impedance of the positive vs the negative input cable leads and the presence of stray power line E-Fields which is a high impedance stray voltage field coupled by the capacitance to each input.
The body itself is like an antenna with a large capacitance from head to toe due to the fluids under the skin, so getting good CMRR for electrodes requires a good low impedance ground and suppression of common-mode signals. The common-mode signals are summed in the RLD amplifier then inverted with unity gain and used as the "ground reference" or 0V reference for Common Mode signals. Since the inverting amplifier has lots of negative feedback, this common-mode error signal gets amplified and nulled and arbitrarily was chosen as the right leg for this "ground signal". Remember that in electronics "ground" just means a chosen 0V reference that does not need to be connected to earth gnd (and is not) for safety reasons on these types of instruments. This means the RLD cable and electrode must be the same length (inductance) and thus impedance as the ECG or EEG signals.
The other way to reduce CMRR is to equalize the impedance of both signals (+,-) is shielded twisted pairs and in some cases use a large ferrite toroid around the cables with multiple turns to reduce the stray coupling of current, but this works better for low impedance signals by raising the CM inductance and thus impedance with higher frequency noise. You will find these moulded plastic clam-shell ferrites on all VGA cables, some battery charger cables and some Electret mic cables.
When you touch the input of a 10:1 DSO probe, you may see > 50V of stray Efield from your body until you also touch the ground clip. Now you are injecting a common signal into both inputs so the result cancels. This is what your ECG/EEG amplifier does with the RLD inputs derived from common mode input signals now inverted and fed back to cancel this input.