I don't know where you are seeing this LIE, but any card with multiple power connectors will flat out refuse to work AT ALL if they aren't both connected.

 Trying to run on one will totally mess up the power circuitry ON THE BOARD to the point the board probably wouldn't work at all and might FRY that power circuitry AND THE GPU AND MEMORY, even if it DIDN'T check for both connected in the BIOS code before the BIOS enables the GPU for actual usage.