i dont think a fuse will cut current from the cig lighter socket, unless its a major short.
the cigarette lighter itself is a coil that basically short circuits the socket, its inherent to the way the electric car lighter works. a short circuit across a poor conductor makes it hot, causing it to light aflame. if the fake charger got a strand of wire (probably from the step-down coils) frayed and shorted, it would've been enough current to heat things to burning but not enough to cause the socket to cut out -- it thinks there's just a lighter at work. too bad there is a lighter, and it's not meant for cigs....