Anthropogenic climate change is increasing extreme rainfall as a result of an increased water-holding capacity of the atmosphere due to higher temperatures. However, observed rainfall-temperature scaling relationships often differ from the theorized increases in moisture-holding capacity. This discrepancy is most evident in the tropics, where higher surface temperatures show a marked decrease in extreme rainfall intensity despite observed increases in extreme rainfall. Here we use atmospheric moisture measurements from the National Aeronautics and Space Administration's Atmospheric Infrared Sounder with surface data to investigate the tropical rainfall-temperature scaling relationship. We show rainfall intensity scales positively with integrated water vapor in all regions. Further, integrated water vapor does not consistently scale positively with surface air temperature and its dependence on background temperature offers a physical explanation for the apparent negative scaling. We conclude that the inconsistent relationship between surface air temperature and moisture is the reason for the "apparent" negative scaling consistently found in the tropics.