According to Jay :
GFI outlets do not work without a proper ground. (The "test" button
trips them, but the plug in tester will not). I know this because I
failed a CO because a GFI was on an ungrounded circuit (knob and tube).

The inspector was either ignorant of the NEC, or, you misunderstood why
you failed inspection.

The NEC (and CEC) _explicitly_ approves GFCIs on ungrounded circuits for
renovation/repair work if you don't have a real ground.

They work just fine without grounds.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.