That was a great video and doesnt apply at all to what would be produced with 120V home wiring. The video produced an arc flash of 25,000 amps according to the title.
When you put a meter set to AC Volts and on a setting that has a range higher than the expected voltage across a hot point and say the ground wire there is no load in the circuit to regulate the current that is the worst case for potential arc flash as it will instantaneously draw as much as the transformer on the pole could provide in the case of a dead short. In the case of fuses they will heat and blow quickly in the case of a circuit breaker they will hopefully open. Huge inrush currents have been known to weld a breakers contact shut. With the fan wired into the circuit the fan is a load and would regulate the amount of current that could go thru the circuit to maybe 2 amps.
Say the failure wasnt the switch and the fan had somehow developed a dead short inside it and removing the switch and touching the wires together would crowbar the circuit. Just as touching a jumper between the screws to test the switch. Doing the voltage tests will tell you the switch is bad or a bad connection as in the back stabs. You can then take the switch out and check it for continuity with a different setting on a multimeter and determine if it was good at the screws and not the back stabs or just buy a new switch and feel safe it wont cause a dead short when you flip it on. My dad used to carry a 60w lightbulb with pig tails and clips. He would have taken the fan down as suggested and clipped the bulb on for a load that would both tell him the circuit worked and also regulate the current when putting the power back on.
Nothing wrong with having some load on a line IMO.