It could be faulty too. But why not have a look at your bios first? Which bios is installed? Before 1.2, the CPU was not supported, that's fact. The c-state can be disabled in bios too, if the PC still shuts down in idle. After these steps, I would consider the psu faulty. At this moment, all possibilities could be true.
If you disable c-states, a non haswell ready psu would work without problems, that's pro
Contra is that the CPU will use more power in idle, but if you wouldn't need to buy a new psu, that's ok.