360A on 12v would be 4320W so that's clearly not posible. The breakers inside my house have a 10A limit if I remember correctly so that means a 2.2kw limit on a single one so I'm pretty sure you could not draw that much power from a single plug.
360A on 1.2v is more realistic at 432W but Ohm's law(I know it as I=V/R) tells us that the resistance on a trace carrying that much current would have to be very, very small and so the trace on the PCB would have to be huge(maybe that's why they say that it has a lot of copper in it). I honestly don't think it's possible, but i'm not an electrical engineer so I cannot say for sure. Maybe someone around here is?
Of course there could be more than one trace...
In any case, video cards this days are awesome feats of engineering in my humble opinion and this card is no exception.