If the charge on a metal object from a voltage source is steady, earthing the object will free one from receiving a shock on touching near or remote from it, provided the other terminal of the voltage source is not earthed. Metal objects with fluctuating charges are liable to give electrical shocks when there is considerable earth resistance.
Earthing one point of a voltage source simply brings that point to same potential as earth. There is no potential to anything else until you introduce a current flowing to another point of potential from the source, whether it be directly by contact with that point or indirectly through other loads.I do not agree with that at all.
Even in ungrounded systems, there will be coupling with the earth and a huge potential difference between the hot conductors and the earth. Dropping one to ground will still establish possibly fatal step potentials.