Please test the other memory slots, if you are using 1+3 now, try 2+4 instead.
Downgrade 2000Mhz to 1333Mhz means that memory will show up as 1333 in the BIOS, until the user sets it to another speed as 2000Mhz is not a speed option in P67/Z68
CPU or motherboard memory support only goes by official specifications from Intel, meaning defaults, you can always overclock the memory and CPU if your BIOS has the options. Intel's $1000 CPU's only say 1333Mhz memory support too, it's just the official specification, but it can mean your CPU is limited by a max memory multi to 1333Mhz at default Bclk if you only have certain memory mulitpliers, then you'd have to raise the Bclk. But your board has higher memory options so that is not something you have to worry about.