There were older shock-protections (especially in the UK) which did measure ground current. These were easily fooled due to the many possible sneak and surge paths.
Most recent US 3-wire GFIs do include Green in a secondary level of protection. White and Green should connect ONLY "back in the fusebox" (many special cases, see NEC). If a GFI detects that White and Green seem to connect "very nearby", it will trip. I observed this without understanding when I kept tripping a GFI in testing. I had an actual problem with the outlet I put right next to my fusebox (2 foot cable); running the cable up and back (say 6 feet) and trying a different GFI "fixed" it.
I will accept that distance may be a factor on some GFI's. My experience with GFI's, began, when you found GFI's in the panel box, not at the outlet. (Outlet GFI's cheaper). Distance definitely less than 2 ft. But it wasn't so long ago, I put a 277/120-0-120 transformer one one leg of wye system 480/277 (60 HP) pump motor control center. We provided three plugs, a 240, and two 120s. (application is very similar to wiring a PT with a CT) The owner wanted to run a small 1 hp pump in the area for various reasons. Even after 3 visits, The journeyman electrician could not wire the GFI's correctly. (He wired a floating neutral). We corrected his wiring by wiring the neutral to ground at the same lug as the green/yellow-green wire. His boss also a journeyman, would not ok grounding the CT of the transformer to ground. It took several phone calls and several days including calls to the local electrical inspectors to get the transformer wired properly. (Instructions did not label the CT point as a CT) The local inspectors wanted the CT point labeled as a CT. Finally got the manufacturer of transformer to supply a schematic showing a CT.
Regarding miswiring, with the same electrical contractor, we bid on a job to provide wiring within a building with three phase power. Only the 10 ton ac was three phase. The electrical engineer called for a wye system. We completed the wiring, provided some plugs for other contractors to do their work. some of the plugs were 208 to ground. Had we completed all the plug installations 1/3 of the plugs would have been 208 to ground. The local power company provided delta three phase.

The mechanical contractor had to replace an $800 board at his cost, and we lost three cordless battery chargers.
The owner also had to pay for a subpanel so the required 120 plugs could be provided. (We also wired the electric water heater 208v instead of 240 volts).
With a pool contractor, we had an electrical inspector insist that we ground the electro-potential ground to the main panel ground. We refused, got a red tag, and an apology a week later from the inspector's boss.
Playing with electrons can be fun as well as deadly.