The Sun and moon both have angles of about half a degree in our sky. Varies slightly with sun-earth, moon-earth distances.
I think what Public heel was trying to say was that to be a truly full moon (not even the tiniest portion un-illuminated), you would have to be exactly between the sun and moon (eclipse). This would be for a point source (which the sun is not). Since the sun has size you could move around from a postition exactly between the sun and moon and still see the moon as completely illuminated. Not sure offhand what the distance would be.