Indoors, it does NOT matter if your electric is connected to dirt. (What you do at work is for much bigger outdoor systems.)
The amp chassis, guitar cord, guitar shielding, and ideally your body should all be at the "average" of all the electrical fields in the room (wiring, lamps, etc).
Measure resistance from guitar cord all the way back to the screw on the wall-outlet. Should be same as touching probes together, dead-zero (or as low as your meter gets). Certainly less than a few ohms. You already tested from guita cord to IEC and that was OK; if g-cord to wall fails, your IEC cord is bad (or you have busted ground somewhere).
Now measure AC Volts from wall-outlet U-hole to the other two holes. Ignore the one that jumps over 100VAC. The other one should be very-nearly zero. If there are other loads in the house, a volt or two is normal. If you have a long feeder (like mine) and run the microwave or toaster, 2V or 3V is not-wrong. However anything over a Volt ground-to-neutral with no heavy loads is suspicious.
What is the history of the house? Built in 1999 with master electrician and sharp inspection? Or farmer-wired bit-by bit in 1909, 1931, 1959?
EDIT I just noticed your Location says Australia. No major difference except "U-hole" may be round and "over 100V" will be headed for 200+V. And I dunno how much idiot-wiring is tolerated there. Still, and as your sparky says, G and N are tied in the fusebox and should be nearly the same at every 3-pin outlet.