You do have to assume at some point that if you fire individual electrons through the dual-slits and record their individual results, that the results are independent. If you can assume this, you're drawn to the current model which is that the electron is in a superposition (i.e. "interferes with itself") that when resolved gives the observed statistical outcome of your independent results. This seems also to be the simplest model (there has been 100 years of trying to find simpler models that reproduce these results).