Or maybe the load screw is cross-threaded and didn't turn easily for their screwdriver ...
It turned easily for me when I fixed it.
You might have more problems than the one you solved. Does the dishwasher have its own circuit breaker, and did it trip for this fire?
It still had 110v when I went to fix it. I found the breaker it was on, and when I switched off the breaker I didn't notice anything else around the house lose power. So yes, it seems like it has its own breaker, and no, it didn't trip.
So you're suggesting that the breaker is bad as well? I.e. not tripping when it should have?
Now that the dishwasher is properly grounded to a real ground (at the electric panel by the ground wire connection), I think the breaker will function as designed. In the previous installation, the high-resistance connection in the connection box turned it into a 110v heating device until the wirenut melted and the two twisted wires fell apart (leaving the connection box energized with 110v). The neutral wire was providing a conducting path back to the circuit breaker, so that worked as designed, but the connection box was not adequately grounded so the current didn't have anywhere else to flow.
If the dishwasher had been able to draw more power (into, for example, the windings of its motor while it was running) or if it had a better path to ground (through the ground wire-- or through you!) then the circuit breaker would've sensed a high current flow and tripped out.
Although if enough current went through you to trip the circuit breaker, that event may have only been of interest to your survivors.
When you "go to fix" an electric appliance, it's always a good idea to start by opening the circuit breaker (or unplugging it, or shutting off the light switch on the circuit) until you find out why the appliance stopped working in the first place. The big, obvious appliance fires are relatively straightforward to troubleshoot (once the fire is out). The little tiny fires that burn out the appliance while leaving only a whiff of scorched insulation-- those are the ones that kill you when you show up to figure out the problem.
A neighbor once gave us a table lamp that had "stopped working". I checked the cord and the switch and the bulb and didn't see anything wrong with it, so I plugged it in (to a receptacle under the table) and switched it on. Luckily I was wearing shoes and sitting on a plastic chair, because the switch shorted out and the entire four feet of cord went up in flames in a microsecond, filling the room with acrid smoke and scorching the table/tablecloth. The event didn't draw enough current to trip the breaker, but it sure generated some excitement. We scampered out of there, opened the breaker, unplugged the lamp, and then opened all the windows to clear the air.
After everyone had a chance to settle down I checked the lamp switch for resistance & continuity with a multimeter, and it seemed fine. I replaced the cord and then took the lamp outside to test. I plugged into a power strip, and the shorted switch did its thing again. This time the power strip fused its own switch and then blew its internal fuse. I replaced the lamp's switch, tested it on a new power strip, and it was fine. But I doubt that neighbor will ever ask us for repair help again...
Of course if a Navy servicemember had brought me that lamp on a submarine, we would have filled a rubber room with insulated electricians and done a thorough job of "deranged gear checks" before turning it on. We probably would have found the bad switch with advanced test equipment (and more experienced technicians). But I was complacent and sure that I knew what I was doing.