I have witnessed this myself !
Last year around this time, flying from Faro to Exeter. It was during the climb, must have been around 20,000 feet or so.
Full moon, directly on my right hand side, and whilst looking down on the ground I could see what looked like a spotlight being shon on the ground.
Rivers, fields, trees, buildings all apeared as if it was daylight for a second or so, and this continued for quite a while (probably the same, around 15-20 mins) then stopped!
Was really strange, but must be some sort of reflection from the moon ???