Well if the moon is an average of 12%, that's a pretty dull. Slightly darker, as you pointed out, than a grey card. That's NOT white like it looks in pictures.
In pictures, and to the adjusted eye, the moon appears rather white...I would say zone VII-ish. Indeed, not blowing out the moon can be a challenge when it appears in a landscape. So yes, the moon is sunlit...but the moon is not white in reality, it is rather dark grey, so if you applied "sunny 16" it would come out looking dark grey. If you took a reading off a grey card in daylight and wanted to place it on zone VII you would meter it and then open up two stops. If you want to place it at the appropriate tone you should apply "sunny 16" and then considering where you want to place the tones, open up slightly to place the moon higher up the scale for a normal, white appearance. Whenever I have taken moon pictures, I have used "moony 11" or "moony 8" and got good results.