Yeh, there's no chance of that.
I made a fresh install of RetroPie on a new card and installed 1 PS game on it. Without going into any drivers or any configs other than to configure the button presses on the PS controller at system startup, the controller worked perfectly in game.
This confirms that there is a config somewhere on the other card that is preventing the PS controller from working in PSX games. I just have to find it now.