I suspect that some writers are confusing the old Voltage Operated GFCIs with the new Current Operated GFCIs. The modern type contain a little toroidal transformer that the live and neutral are threaded through. Normally the go and return currents are equal so the transformer does nothing. If the currents are not equal the transformer produces voltage which operates the trip relay and cuts off the power.
The old type of GFCI uses an earth rod. The house earth wires connect to one end of the trip-coil of the GFCI. The other end of the trip coil connects to the earth rod. If anything in the house leaks current the GFCI will turn off the power. The problem with this type of GFCI is that electrical storms can blow the trip coil. This leaves everything in the house un-earthed and with no GFCI.
One delightful property that I was asked to "look at" was giving everyone electric shocks. The floors were concrete and the bungalow had a voltage operated GFCI with a blown coil. I suspected that the immersion heater element had also corroded and was now pumping current into the hot water system. Water taps, light switches, the kitchen range and anything metal that was supposed to be earthed were all live! The property was owned by a penniless widow and there was no money to do the job properly. Power was supplied from a pole-transformer dropping the 11,000 volts to 240 and with these the neutral is always earthed at the pole. After checking all the legal stuff it was decided to use PME (Protective Multiple Earthing) A heavy duty wire link was connected between the Neutral and the Protective Conductor (AKA "Earth") on the fuse-board where the power entered the building. Result no more electric shocks! I did that "bodge" about thirty years ago and its still working fine. Sadly the widow passed away long ago. She died of old age not electrocution.
IMHO those voltage operated GFCIs that date from the 1950s and 1960s ought to be banned. They probably are but people still use them.
One old house that had its wiring fixed by a friend had a two wire (live and neutral but no earth) system where the wires were let into grooves in wooden conduits. A mouse had caused a short and blown a fuse. If the Electricity Board had seen the antique wiring they would have demanded a full re-wire which would have cost thousands! Take care!