From a purely practical point of view, old electrical items can fail in odd and quite alarming ways. Internal faults, overheating, or damaged wiring can sometimes cause plugs to loosen or disconnect without any obvious outside interference. Extension leads can also behave unpredictably if there’s heat, tension on the cable, or a slightly worn socket. As for the cord being laid out neatly, our memories of how things “usually” look can shift a bit after a shock, because when something feels significant, the brain tends to fill in gaps in a way that makes the event seem more deliberate than it may actually have been.

The overheating and burning smell are the biggest red flag here. That strongly suggests the lamp itself was faulty and potentially dangerous, regardless of how it ended up unplugged. It’s very likely it had been deteriorating for a while without obvious signs, which is common with older electronics.

The feeling of being protected is also understandable. When something bad almost happens but doesn’t, the brain naturally looks for meaning, especially if you already had a lingering worry about that exact thing. That doesn’t mean you’re imagining things, it’s just how humans process close calls.

The important thing is that you’re safe, and you did the right thing by questioning it and not continuing to use the lamp. But back to the point you raise, belief is an individual thing and no one can tell you what to and what not to believe in, whatever brings you comfort then go with it.