Dangers of bootleg ground and GFCI?
If you don't trust a ground, don't connect to it - use GFCI instead. 

If a GFCI won't trip with its own internal test button, it is duff.  Into the trash it goes.  

Here is how GFCIs and ground wires are supposed to relate to each other -- or to be more precise, how they are not.  



To the left you see unprotected hot and neutral coming in, out the right you see protected hot and neutral, which I've recolored.  Ground sails right by unconnected (normally).  Obviously, if your ground is corrupt/defective, this is bad news indeed. 

"Wait, all the GFCI's I've ever seen have a ground screw."  No.  That thing you call a GFCI is actually a GFCI+receptacle combination device.  It provides a GFCI module, and also two sockets (wired past the GFCI). The GFCI can't use ground. Look at a GFCI breaker, it doesn't even have access to ground. The ground is for the sockets.  This means effectively, that ground screw is on the "protected" side of the GFCI. 

So if the ground is bad, where should you cut the ground?  Before it reaches any protected loads, and remember, the ground screw on a GFCI+receptacle combo serves the protected loads.

Should you do anything creative like tie the protected-side ground into protected-side neutral? No No No! This post of mine explains how that utterly defeats the GFCI protection.  Wrap the ground wires with tape so they can't touch, and don't use them. 

Detecting tied ground-neutral

If your panel is set up this way, the single easiest way to test your neutral-ground isolation is to disconnect your neutral-ground bond in your main service panel.  Now the only thing connecting neutral and ground is that long path of dirt between your grounding electrode system and the pole transformer's. If you also unhook your grounding electrode, your house's internal grounds should be fully isolated from neutral, and should megger out at a couple megaohms.  (Don't megger things in residences though, it could fry electronics).

Or test circuit by circuit.  It's a simple thing, on any given circuit there should be 0.000 amps of current flow on the ground wire. Nothing is supposed to use ground but test equipment.  Now, if neutral and ground are tied together, current follows all paths in proportion to their conductance (1/resistance) so a significant fraction of current will take ground instead of neutral (assuming there is a load).   Obviously a GFCI will detect the shortfall, but a clamp meter will detect the ground current directly. 



I don't agree with that video's claim of nearly 1 ohm between neutral and ground. Copper wires have much better conductivity than that unless he has many hundreds of feet of wire between his lab and his main panel. There may be something peculiar going on in his test lab, or he is misunderstanding or misusing the equipment. You shouldn't have 1 ohm neutral-ground, that would limit dead-short current to 120A, which would not flow enough current to safely magnetic-trip a breaker.  

In any case, a clamp ammeter around the N-G bond (or a circuit's ground wire) would soon show if any AC current was flowing.