i think we're both wrong. the moon reflects only 7% of the sunlight that hits it, but it sends out approximately 400,000 times less light (14 magnitudes dimmer). I had to get someone smart to explain it to me.
To put it another way, only 7% of the sunlight that hits the moon gets reflected. But of that 7%, only a tiny portion gets reflected such that it intersects with the earth since it is radiated in all directions, so we only capture a very tiny percent of that 7%.
By analogy, it would be the difference in light between staring into a flashlight at night and seeing the light of that same flashlight reflected off a not-particularly-reflective distant object.