Models and physical reasoning predict that extreme precipitation will increase in a warmer climate due to increased atmospheric humidity. Observational tests using regression analysis have reported a puzzling variety of apparent scaling rates including strong rates in midlatitude locations but weak or negative rates in the tropics. Here we analyse daily extreme precipitation events in several Australian cities to show that temporary local cooling associated with extreme events and associated synoptic conditions reduces these apparent scaling rates, especially in warmer climatic conditions. A regional climate projection ensemble for Australia, which implicitly includes these effects, accurately and robustly reproduces the observed apparent scaling throughout the continent for daily precipitation extremes.