I don't think diodes on the ground lines would be the way to go, but either way...wouldn't the Ground on the Extra PSU be connect whether or not the Extra PSU is turned on? (Assuming you're not unplugging it all together) That would mean, for example, that if you've got a button set to be 'red' when the computer is turned off (by connecting the RGB-drive red ground to the Extra PSU ground), that even when the computer is on, the red part of the RGB will always be on.
I'm assuming Randy was talking about diodes on the 5V lines to prevent power from going from the Extra PSU, bypassing the resistors in the RGB-drive entirely, and directly into the LedWiz, which would probably be bad.
There's probably a more elegant way to do it, but seems like what would work would be to use transistors on the ground lines to open or close them based on the power coming off the PC-PSU 5V line.
* I only took one semester of electronics. My career is in biology. These guys are almost sure to know more than me. Listen to them.