From Dave's description of that junction box, it sounds like there may be no ground connection through to the Mains inside the coach. Nevertheless, the fault should have blown the breaker at the post outside; those in my experience are often faulty.
Factory personnel, as we all know, commonly drop wire ties and screws without taking time to retrieve them. But 3 screws at the bottom of a small j box implies a very clumsy or incompetent employee, or a poor repair or retrofit by someone later - perhaps an indication of an unprofessional attempt at wiring also, and by inference the wire nut scenario others here have experienced.
The scary thing that should indeed spook Dave is if there is no metal conduit between the j box and the 50 amp main box inside, or no modern wiring to it in lieu, then theoretically he never had complete ground protection for any device or appliance in his coach. The wire he's seeing could be from either the Main end or the cord end. Sans metal conduit, I'd expect to see two wires grounded to the box, not one. It's probably simply the cord ground, thus the arcing to the box from a bare hot lead. The post breaker may have tripped, just not before sparks caught some debris that smoldered ultimately into the plywood structure behind.
Otherwise if the j box got hot enough to ignite the wood, then you'd think there was enough errant current to have kicked the breaker before that it got to that point, and I'd point at a faulty post breaker as contributory.
Reckon we'll have to reserve judgement for all this until an electrician clues him in more.
Not sure why the electrician did say heavy AC use affected it, if it was a direct short within the j box.
Joel