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It seems that your system has hard times with the memories... It means that could be a problem with the memories itself, with the DIMM slots and with your CPU - yes, your CPU, since it has a memory controller built in.
To start with, the Corsair memory kit model #CMZ32GX3M4X1600C10 is listed being compatible only on the Corsair's site - meaning that only them tried it, Asus didn't. So, if you could try first this kit in your friend's system would be nice... Just to be sure that the kit is working...
The other thing you could do, is try each module in each DIMM slot (doing 2 cycles of Memtest for each variation) - this way you can figure out if there is a problem with either the memory kit (one of the modules) or one of the DIMM slots.
And you also have to check the pins in the CPU socket... if the pins responsible for the memory controller are bent, you will see it as a memory problem...