You're not actually wrong. The twinned rainbow of youtube video fame are concentric and explained by the different sized droplets. The other type is essentially made from the twin suns of tatooine, one of them being the reflected sun off the water or other highly reflective surface and the other being the regular old, American sun.
Glatt, isn't always right. There was that one time that he thought he was wrong, but it turned out that he was actually right.