First your created a serious human safety problem. No wire
must connect to a pipe to dump electricity in that pipe. The
electrical inspection probably failed because an outlet
without ground did not have the necessary (code required)
label "No equipment ground". So instead, you created a threat
to human life.

GFI works when test button is pressed because that is how a
GFI works. Electrical inspector simply discovered a missing
ground on a three prong plug without any indication of that
missing ground - a code violation. He did not fail the GFI.
He failed the missing safety ground. Now for that pipe
problem. Again, you have created a human safety problem
especially for people standing in water in a bathroom.

The idea is not to pass the inspection. The idea is to make
a safe house.

Jay wrote:
A GFI in our bathroom failed with the "tester" because there was no
ground. I grounded the outlet with a clip-lead to a copper pipe,
and the GFI worked fine.

So, in theory, I agree that a ground is not needed. I'm not sure
that is true in practice. And the best response for a Code
Inspector is "Yes, Sir". :+)

Do they make "two prong" GFCIs? I guess the GFI "breakers" are the
best answer (except for the trip to the basement everytime one
trips).