Nah, memory is very rarely the issue. In this case, perfectly normal to need to set 1600Mhz in BIOS on an AMD platform, for example. Depends on the cpu/motherboard you used but almost certainly the RAM is fine.
1333 is most likely the highest speed your CPU officially supports. The BIOS will default to not overclock. To overclock your memory controller to use the ram at DDR3 1600 speed you will have to do that in the bios.
That's pretty standard. You probably have to fish around in the BIOS for the memory settings and then manually select a different SPD profile with 1600 MHz timing. Also watch when you upgrade the motherboard's BIOS in the future, as it may reset the memory timing.