Finally, someone who understands how GFCI works. I've talked to licensed electricians who do not understand this.
This is why GFCIs do NOT protect you from electrocuting yourself if you touch the hot and neutral on the same device. No current is leaking to a "ground" outside of the circuit.
What the OP described is working exactly like it is supposed to. Assuming he is shorting the hot to the neutral, then the panel breaker should trip and the GFCI should not. This is actually a valid test I suppose, to make sure your GFCI is working correctly.
A lot of people also think a GFCI needs to be connected to ground to work correctly. Maybe GFCI is a bit of a misnomer because it confuses a lot of people. Instead of GFCI maybe it should be CLCI - Current Leak Circuit Interruptor. Or EGFCI - External Ground Fault Circuit Interrupter.
We all know how a gfci is supposed to work. The doesn't change to fact he putting a piece of wire on the plug to attempt to test it(which of course won't work). The rubber grips on the pliers make it ok though. Anyone actually ever read the grips on your Klein's. They say warning does not protect from electric shock and I highly doubt he was using a tool with a quality comparable to a real trade tool.
Sarcasm is my friend
I'm here to learn too, i do mostly commercial/industrial/new construction and this place is a great way to pick up tips on residential from some good electrical minds. Excuse the spelling, my phone has a mind of it's own.