The problem could still exist with a 'genuine' 5v charger that uses a buck DC to DC converter to convert the car 12v into 5v.
The fuse, usually located in the 'Nose' of the cig lighter adapter is fusing the 12v in, and limiting the input current to 2A, a power into the adapter of 24W. The adapter should be designed to limit the output current, often to 1 amp or 2 amp, while still delivering a controlled voltage of a little over 5 volts. Enough over so that it's still 5v at the end of the cable run.
With an efficiency of most of these little adapters being about 90%, 5 volts out @ 2 amps, 10 watts out would only need 11 watts from the car. While it looks like a 1 amp fuse (12 watts in) would be better, start up current for these converters can surge to get it up and running.
Another thing to consider is the voltage at the cig lighter plug is a little more than 12 volts.
2 amps (5v) output is needed by some devices, but something would be wrong with the Mobius camera if it was trying to draw 2 amps.
There are a few possible failure modes that would overheat components and generate enough heat to melt the plastic case.
Overcurrent.
This failure mode of course would be a failure of the adapter to limit output to 2 amps as designed.
This would be a secondary failure as the Mobius would not normally draw more than 2 amps (see below).
Overvoltage.
The adapter could fail to regulate the output to 5 volts. Here we could have a higher voltage or a lower voltage as a failure mode.
A lower voltage, say 3 volts could fail to properly start circuitry inside the Mobius camera and as a result some components might not be functioning optimally.
That would usually isolate failures to just a couple components, letting the magic smoke out of them but not generate heat over a large area of the circuit board.
A high voltage failure could cause internal components to overheat (if there is no input protection). With more power being available the circuit damage could be more widespread. Once a power control, power conversion, or power consuming component fails, other components could also fail causing additional heat damage.
A 'small' adapter might also have visible damage but a larger more capable adapter may not show any damage externally. IF the adapter supplied excessive voltage, was it a component failure (usually permanent) or a LOGIC failure of a smart charger?
One question to be answered, did this model of the Mobius have the input overvoltage protection circuitry? A primary cause of overvoltage from the adapter would not cause additional secondary failures inside the Mobius camera.
Mobius component failure.
One failure mode would be no fault of the 12v to 5v adapter but a component failure internal to the Mobius camera causing excessive current to be drawn.
Even 2A in this case would be excessive. In a camera system like the Mobius, there are several subsystems that generate some heat. The processor obviously gets quite warm as there are heat sinks over it. The image sensor generates some heat. But from the photos of this failure it appears most of the heat was generated close to the flatpack chip and components close to it. The inductors connected to that chip appear to be part of an internal DC/DC converter. Possibly to generate the various operating voltages required internally. Once this subsystem failed and was consuming most of the input power those components got very very hot. Hot enough to heat the circuit board nearby. Hot enough to melt the plastic case. 10 watts of heat (5V times 2 amps) in a small localized area can create some rather high temperatures. With no place to go (semi-sealed plastic case) heat would continue to be generated until the current ceased flowing.
Now, did this camera subsystem fail because a local component failed, or another internal subsystem was overloading it, or was the input voltage greater than the circuit was designed for?
