Originally Posted by
watercooled
In which case I suspect OCP even more, the PSU is divided into 4 12v 'rails' of 16A max each, so 192W. If the 4870 is drawing all the current from a single rail it could be tripping the OCP, causing the PSU to reset. I still wouldn't pay any attention to the voltage readings to troubleshoot, besides you'd expect the voltage to go down, not up, under heavy load and <1% over spec shouldn't cause this.
How exactly have you got the card wired up, which connectors are you using, etc?
Edit: I've been doing some research on this particular PSU and, as if to deliberately prove me wrong it's a dual transformer design. :D I'll read into it more and see how the rails are divided, maybe one transformer is handling everything so being overloaded?