Just to add another twist...
It kept reporting 1067Mhz when I paired the 8GB OWC DIMM with one of the 2GB Apple DIMM's. No black screens.
I happened to have a 4GB PC3-12800 laying around, so I installed the OWC 8GB DIMM on slot-0 and the 4GB in slot-1.
Both reported at 1600Mhz, and black-screen as soon as I started playing a Flash video.
I am not an expert on the new systems but from my it is my understanding that when the Intel CPU based main board boots up with a pair or pairs of memory sticks it will register the timing and Mhz of the memory installed in first slot (in this case probably slot-0) of the two...OR depending on the board it may read and set itself to the lowest speed of the two.
To maintain memory timing compatibility this would mean that slot-1 should run with the same Mhz and timings as slot-0... OR in the case of some systems... the system will downgrade the speed to the slowest speed and timings it is reading from either slot. I'm not sure about how these Mac Mini boards adjust but I am pretty sure they read the memory slots and adjust one way from slot-0 or the other...setting to the slowest memory installed in either slot.
From your post above it would seem that the memory is posting with the system based on the settings it is getting the memory settings from slot-0 and setting to the speed and timing of the memory installed in that slot which is why the PC-12800 memory would also post as running at 1600Mhz if it is in slot-1. The GPU is probably mapping its required shared memory to the stick installed in slot-0 when both slots are used.
You probably also want to be using a pair of memory sticks that run at the same voltages...either 1.5v or 1.35v. Check the voltages for the stock Apple sticks and the OWC sticks just to see if this is an issue.
If all the memory is working and if it also works in other compatible Intel systems then it has to be either a compatibility issue or there is a chance you could have a defective memory controller that is not allowing the higher speed and timings of the OWC sticks. If you have a late-2012 model Mini with HD4000 graphics then it should be capable of running compatible DDR3 RAM at 1600Mhz.