I'm not buying it either. I've been tromping woods for over fifty years; 45 of them with the bow and have never seen a significant difference during full moon phaze. If anything, they just browse more during the day, especially in whitetail cover....thick undergrowth within their range.
I think folks who keep using the same stand over and over will see fluctuation, but I belive it's due more to food changes in the woods and fields, or just shifting patterns. You keep stinking-up the same spot all the time and the trees would probably change areas if they could 8^).
However, I do think it is a good excuse to fall back on if you aren't seeing deer. It may bring them to the fields after dark more often, but I don't hunt the fields.