You first need to understand there are similar terms that need to be used properly. A "grounded wire" or grounded conductor, is commonly called the neutral. A grounding conductor is commonly called the ground. So, with that said, yes, grounded wires (neutrals) are required for GFCIs to operate. Grounding conductors are not required.

Not exactly. There are 240 volt GFCIs that do not involve a neutral. The only necessary conductors for proper operation of a GFCI are the circuit conductors. For 120 volts, one of those conductors is the neutral.

To put it simply, if you just have the two wires, black and white, the GFCI will work. In fact, a GFCI is recommended in this situation because it will provide protection even though you have no equipment ground.

A GFCI measures any current difference between the live and neutral wires. If they don't match, current is going somewhere it isn't supposed to and it trips. It doesn't require a ground to do that.

put simply, in any situation posing a threat to human safety, a gfci will trip instead of shocking you. this functionality is not affected by the presence of a ground.

first electrician wrong, second right. if you buy a gfci outlet it comes with a sticker to be specifically affixed when the gfci has no ground, so there is a way to know. so put on those stickers!

a final thought: retrofitting two wire with GFCI's plus the usage of a whole-house surge protector is a fantastic alternative to rewiring.

OK, first off, I was mixed up. I meant to say the first guy is wrong. Sorry 'bout that.

Second.
civ_IV_fan, a GFI will not prevent a small shock (pain). It will prevent a sever shock/electrocution (death).

"put simply, in any situation posing a threat to human safety, a gfci will trip instead of shocking you. this functionality is not affected by the presence of a ground."

And it may provide NO PROTECTION if you are across the hot and neutral on the load side of a GFCI.

Most of the time you have a ground connection that unbalances the hot-neutral through the GFCI, but it is possible to be isolated enough to not leak current to another path.

the first electrician was an inspector and knows his plug in testor doesn't work without a ground wire, therefore he thinks the gfci doesn't work. silly inspector!

"the first electrician was an inspector and knows his plug in testor doesn't work without a ground wire, therefore he thinks the gfci doesn't work. silly inspector!"

The plug in tester is not even a reliable way to check a GFCI.

The 'TEST' button on the face IS the recognized way.

The small testers do not have adequate precision in the 'leakage' current they simulate.
They are a 'meatball' way of verifying that a regular receptacle is on the LOAD side of a GFCI.

They put a load from hot to ground to unbalance the current.
No ground, no current, but it has nothing to do with the GFCI working correctly.
They put the unbalance around the sense coil between the hot and neutral.

You can always use the method the guy I worked with used to use. Lick your thumb and then touch the non-grounded conductor. The GFCI ought to trip (unless you manage to bridge yourself across the two protected conductors).

(Admittedly this was before the days of GFCI's, it was how he detected the hot bus).

I might add that my wife can testify that you still get shocked off a GIF circuit before it trips. She forgot to unplug the coffee pot while cleaning the inside and rested one her arm on the stainless steel kitchen sink .... Ouch!