For any public supply one of the key criteria is that the neutral of the supply is solidly referenced to earth and this shoudl be maintained in all circumstances.
Therefore any connection of neutral and earth on the consumers side of an installation must give two parallel paths: one via neutral back to the supply and one via earth back to the supply.
If you have two circuits on the same installation and consider the case for each main earthing system.
One circuit is off via the circuit breaker and has the neutral and earth connected together.
The other circuit is on and operating normally.
Current from the second circuit splits at the neutral bar down both Brown (normal neutral current) and purple (alternative via earth) paths according to the relative resistances of each path.
Purple is the lowest resistance and brown is always higher.
All earthing systems will have the neutral to earth resistance of the circuit with the touching NE as a part of the resistance of the brown path.
So for TNS you are comparing supply neutral conductor and the supply earth conductor, both similar.
For TNCS you are comparing Neutral bar to PME link and earth bar to PME link, extremely similar
For TT you are comparing neutral supply conductor to RA, RA is much higher.
Therefore for TNS and TNCS the neutral to earth resistance of the circuit will be the factor that lowers the current via the fault path and for TT the current via the fault path will be much less than that via the normal neutral.
So long as the current flowing via the faulted circuit neutral is greater than 30mA the RCD will trip, as there is no current flowing in the line. This current is proportional to the load current and the relative resistances of the two paths.
Even if only 3% of the current passed via the faulty circuit neutral then 1A in use anywhere in the installation would be enough to trip the RCD protecting the circuit being worked on.