More importantly, why does it matter that you hook the ground wire to the ground of the button?
As I was about to reply, "Go ahead and just hook wires up to it and see which way works." I proposed a question to myself, is there any reason that the buttons have there inputs labled GND and NO other than if you would want to A) have two inputs hooked up to it, one NO and one NC or B) have just one hooked up to NO or NC and you just need to tell the difference.
The way I see it is that the only thing a button does is complete a circuit, there are no polarities when it comes to a simple switch such as an arcade pushbutton right?
If it were me, I'd just hook it up and see which way works. With only three prongs and not taking polarity into consideration that only leaves 3 posibilities, (A&B) (A&C) (B&C)