My 5820k recently died, must have been the memory controller.
My problem manifested as a "ram" problem, but corsair supplied me a new kit under warranty and it behaved the exact same as the old kit.
Initially my system would run with "load optimised defaults" (i.e. stock), but the symptom arose where it could get to bios but not OS, it'd just hang or reboot, sometimes the BIOS was missing one stick. I noticed that enabling XMP resolved this and the system became bootable. My immediate thinking was "ok this must be because xmp increased ram voltage". I tried numerous settings (including ram voltage alone) which didn't work. Only enabling XMP helped. One day the PC just came on with a black screen, no post, no bios, did all the usual clear cmos, re-seat ram, etc. I knew I either had a board or CPU problem at this point but wasn't sure which.
You've ruled out the board. IMO you're correct in saying it's unlikely for 2 ram sticks to just go bad, I had the same feeling when I was testing mine. If the memory controller on the CPU is going faulty it'll give you these "ram" issues.
Anyway, intel replaced my CPU. Works perfectly now, same board, same ram, stock settings or XMP, doesn't matter which. Definitely a dead CPU. I still have absolutely no idea why enabling XMP allowed the system to boot when it was starting to go faulty, that one is a mystery to me.