Buddhism merely states that there's a psychological continuum in which there is nothing unchanging. The "self" that's precluded is just an unchanging one. (That said, in the Abhidharma there are unchanging elements from which this psychological continuum is constituted.) The Mahayana doctrine of emptiness (which isn't common to all Buddhism, just the schools that are now found in the Himalayas and East Asia) essentially states that everything is without inherent existence; things only exist as conditioned phenomena in relation to other things, nothing can exist in or of itself because this would preclude change. It's essentially a restatement of impermanence (everything is subject to change) with the addition of interdependence. So I'd imagine few Buddhists have convinced themselves they don't exist.