Short circuit when probing live ATX power supply primary section with voltmeter
I'm not sure what the big inductor is for.  It doesn't look like part of an EMI filter to me, since that would typically be a common mode choke with four leads, and this apparently has only two.  (That's probably a common mode choke on the circuit board next to the the torroidal inductor, labeled FL3, with the white bobbin and the ferrite core.)  It's also rather large for that.  My guess (and it's only that) is that it may be part of a power factor correction circuit.  BTW, "HI POT" is short for "high potential", and generally just means that it has passed an insulation breakdown test.

I don't have any really great theories about the short, except to say that, especially if you're running on 230VAC mains, the peak voltages in such circuits can be quite high, especially in circuits with big inductors.  So it's possible that you didn't even make true metal-to-metal contact but simply decreased the air gap just enough to cause an arc.

Re the isolation transformer, YES, there is a difference!  Please use the isolation transformer!  Disconnecting the safety ground lead on the equipment under test doesn't remove the potential between the hot circuit and earth ground, so you are still exposed to danger.  Even with a well-insulated, floating DMM, you can still have an accident.  Sometimes engineers will float the ground on oscilloscopes so that they can probe line-side circuits, but this is still dangerous.  An isolation transformer is the only reasonably safe way to work on these things.