You should be aware of the difference between GFCI and "grounding". I once had an electrician, who referred to himself as a "master electrician" (whatever that is), tell me the GFCI won't work without a ground wire. Just shows you can't always trust an electrician either.
GFCI can't "make up" for a missing ground wire. It can't turn an ungrounded outlet into a grounded outlet.
What grounding does is supply a path for electricity to flow if it finds its way out of the normal path in a fixture. For example, if you have a lamp or power tool plugged in, and there is an internal failure, for example a loose wire inside touches the exterior metal part of the lamp, then that current will be shunted down the ground wire, if the lamp is properly grounded.
A different situation is when there is something external - such as water for example - that can be a path for electricity. For example you're standing in a puddle in your lawn and you touch a hot wire, or a metal casing on a tool that is touching a hot wire. In this case the GFCI circuit will detect that more current in coming into the hot side than is leaving the neutral side, and it shuts it off. Grounding will not protect you in this case.
GFCI will not protect you from getting electrocuted. It only protects you from current leaving the circuit. For example if you stick a key in the right slot of an outlet and a key in the left slot, and then grab on with your right and left hands, the GFCI is not going to turn off because current in = current out.
I'm sure you can imagine other scenarios and all points in between, but the bottom line is the GFCI and "grounding" do 2 different things.