No, no, no. That kind of setup is illegal right there.
No, he has a weird double fault condition where there is a secondary distribution panel and it loses its earth connection. Each circuit is fused for the wires involved. The big heavy equipment has a Live-PE fault, but can't blow the breaker because the PE is disconnected. However, if some other small circuit on the same distribution panel has an accidental earth connection, the fault current can flow through there to earth, and back up the main building grounding rod. I think this condition is possible in the US. I have definitely seen breaker panels that have circuits of different sizes, although I only know for sure I have seen it in a primary distribution panel, not a secondary panel.
Nevertheless, it is a stupid problem. It shouldn't be possible to lose the earth wire without losing the live wires as well. That is why PE must always be run along with power wiring, in the same conduit or cable so that if something cuts the earth wire it also cuts the power. It is also why you never switch or disconnect the ground except for an outlet which should be designed to always connect ground first and disconnect it last. Saying that shoddy wiring is dangerous is a tautology, and the answer is not to avoid accidental earth connections, but to do your wiring properly.
People do not touch equipment too often.
People touch household appliances essentially every time they use them. Since the scenario you describe won't flip any breakers or otherwise shut off the power, it will persist until someone is electrocuted.
In Russia the most painful thing is retrofitting water boilers in old buildings. The pipes are made from steel and are earthed (poorly). The PE wire is retrofitted and thus cannot be fully protected from mechanical breakage. The boiler connects to both PE and steel pipes and may make a "parasitic" earth connection. The one and only way to avoid this is to use plastic dielectric inserts in the pipes.
The reason steel pipes are earthed has nothing to do with the live-chassis fault problem. All large metal structures within a building should be earthed for potential equalization to avoid large induced voltages due to nearby lightning strikes, power lines, or whatever. They do not need to and should not be relied upon to carry the full fault current of an electrical circuit, but adding a plastic pipe section to avoid running a proper PE wire is kind of insane. And it is a hopeless cause anyway. Maybe with something simple like a water boiler you can avoid inadvertent ground connections... but what happens when someone decides they need an alarm for if the boiler temperature drops, and they hook up a serial cable to a PC. Now your ground connection is through the little foil shield of your serial cable. For many appliances it is even harder. The correct solution is to run a proper power cable that has the PE bundled with the live and neutral. If you can't get a good earth connection, you need to switch to alternate protection measures like RCDs with the associated annoyances.