I have a dedicated 3w blue led, running on a dedicated 300mA dimmable driver. It is set to dim according to the moon phase, using my bluefish controller. At "full moon" it is set to 40% (which is approx 15%-20% of what the 3w LED can put out if fully powered). I have not seen any adverse affects due to the moonlight. I don't think it has enough intensity to do anything other than shine some light on the reef.
I could see if someone were to use their primary lights at a mid level intensity, that it could cause problems, by letting the photo period run too long.