Classic case of overthinking the question.
@OP: Your original assumption (and hence the title) is wrong and misleading. Touching or cutting the CPC ('earth') of a circuit, regardless of whether the circuit is energised or not, does not trip an RCD. Therefore, there is no question to answer about why touching the case of an appliance does not cause this. As others have explained, it is making contact with the neutral that is the issue.
Re post 15, the assumption here is not correct either. If there is a potential between neutral and earth at the origin, e.g. with a TN-S system, even without load on the system the RCD might still trip when N & CPC are shorted by cutting the cable. If the installation has load on other circuits (which need not be on the same RCD or CU) it is more likely that there will be enough p.d. between N & E to pass a current above the trip threshold through the N-CPC short.