Rain isn't in a constant amount, and is not concentrated on a single area. If rain gravitated to fire like a magnet, then this would be true, and I'd say it'd only be logical for it to hurt Fire-types.
However, rain just scatters and falls wherever, and in small doses, Fire actually gets more intense from Water, since it feeds off of the Oxygen found in small amounts of water.
In summary, consider this: When rain falls, every drop of water doesn't attract and bomb you like some angry wasp; nor would rain attract and pile up on Pokemon like Charmander and Infernape. =D