They work just fine without grounds.

OK. Let me correct this. The "tester" failed to trip the GFI. Maybe
it would work if you jammed a fork in the slots or something. I wasn't
about to argue with the Code Inspector for a $10 fix.

Ah.. That's different. The test-device failed to trip the GFCI
because it tried to produce a ground-fault to the ground plug.
The GFCI didn't trip because there was no fault.