That's not a good counterexample because rain comes down. Water vapor, which goes up, is actually lighter than air by a large margin (0.804g/L versus 1.225g/L) at the same temperature and pressure.
Liquid water is certainly denser than air, and the fact that it vaporizes before rising up into the atmosphere is immaterial to the point that it ends up there anyway. The process (evaporation and subsequent fluid mixing) is not significantly different from the process which puts ozone in the upper atmosphere.
