We propose that the natural rate of unemployment has an active role in the business cycle, in contrast to the prevailing view that the rate is essentially constant. We demonstrate that this tendency to treat the natural rate as near-constant would explain the surprisingly low slope of the Phillips curve. We show that the natural rate closely tracked the actual rate during the long recovery that began in 2009 and ended in 2020. We explain how the common finding of research in the Phillips-curve framework of low – often extremely low – response of inflation to unemployment could be the result of fairly close tracking of the natural rate and the actual rate in recoveries. Our interpretation of the data contrasts to that of most Phillips-curve studies, that conclude that inflation has little relation to unemployment. We suggest that the flat Phillips curve is an illusion caused by assuming that the natural rate of unemployment has little or no movement during recoveries.