If the coaxial line is matched to its equivalent differential load, then the voltage source "sees" an input impedance which is purely resistive (50 Ohm). This allows us to greatly simplify this circuit thus making further analysis easier. The trick is in moving the source toward the load "through" the coax. The picture below show the source half way to the load.
Note that an inner wire in the left half of the coax can be left floating or can be shorted to its shield. Finally we have our source at the load side, like in the next picture.
Strictly speaking, the last circuit is not fully equivalent to the first one. Going through the coax, a signal is delayed and attenuated. However, the attenuation is usually small on HF and in most cases can be ignored. Or one can adjust the source level to account for this. The delay is important only if there is more than one RF source in the system, or if a single source has more than one way to the load. In our case an absolute phase (or delay) of a single signal going by the only way to a single load is of no interest. What we have now is in the picture below.
It is clear, that if Z2=0 (grounded load) there is no common mode current through the coax shield. In all other cases we have to solve a simple equation to find this current.